Method and system for applying nmr pulse sequences using different frequencies

ABSTRACT

A method and system for applying nuclear magnetic resonance (NMR) sequences to a substance are described herein. The method includes applying an NMR pulse sequence to the substance using a non-resonant transmitter circuit. The NMR pulse sequence includes a first pulse sequence segment applied at a first frequency to a first shell within the substance and a second pulse sequence segment applied at a second frequency to a second shell. The second pulse sequence segment is initiated before the first shell reaches thermal equilibrium. In some cases, the first pulse sequence segment and the second pulse sequence segment are interposed within each other. Such NMR pulse sequences, with multiple pulse sequence segments, can also be applied to different atomic nuclei.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Patent Application Ser. No.61/608,457 filed Mar. 8, 2012, which is incorporated herein by referencein its entirety. This application is also related to U.S. patentapplication Ser. No. 13/774,425 filed Feb. 22, 2013 (Attorney Docket No.IS 11.0786-US-NP), entitled, “Method and System for Applying NMR PulseSequences with Interacting Shells.”

TECHNICAL FIELD

This disclosure relates to nuclear magnetic resonance (NMR) and, moreparticularly, to using nuclear magnetic resonance (NMR) for determiningproperties of substances.

BACKGROUND

Nuclear magnetic resonance (NMR) can be used to determine properties ofa substance. An NMR procedure typically includes applying a staticmagnetic field to the substance. The static magnetic field generates aninitial magnetization of atomic nuclei within the substance. Then, anNMR system is used to apply an oscillating magnetic field at aparticular frequency to the substance. The oscillating field is composedof a sequence of pulses that tip the magnetization of the atomic nucleiaway from the initial magnetization. The sequence of pulses can bearranged so that pulses and the static field interact with the nuclei toproduce a resonant signal composed of “echoes” within at least a portionof the substance. The portion of the substance where the resonant signalis generated is known as a “shell.”

The resonant signal is detected and then used to determine NMRproperties such as T₁ relaxation time, T₂ relaxation time andattenuation of the signal due to molecular diffusion. These NMRproperties can be used to determine the properties of the substancewithin the shell.

The pulse sequence is typically repeated a number of times so that theresonant signal can be more accurately determined. The next pulsesequence is not initiated until the atomic nuclei within the shell reachthermal equilibrium and are aligned with the initial magnetization. Insome cases, it may take several seconds (e.g., 10 seconds) for the shellto reach thermal equilibrium. This means that the NMR system sits idlewhile the shell reaches thermal equilibrium. This is a particularproblem in NMR borehole logging applications where idle time is costly.

SUMMARY

This summary is provided to introduce a selection of concepts that arefurther described below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used as an aid in limiting the scope ofthe claimed subject matter.

Illustrative embodiments of the present disclosure are directed to amethod for applying a nuclear magnetic resonance (NMR) sequence to asubstance. The method includes applying an NMR pulse sequence to thesubstance using a non-resonant transmitter circuit. The NMR pulsesequence includes at least a first pulse sequence segment applied at afirst frequency to a first shell within the substance and a second pulsesequence segment applied at a second frequency to a second shell. Thesecond pulse sequence segment is initiated before the first shellreaches thermal equilibrium.

The first pulse sequence segment generates a first resonant signal inthe first shell and the second pulse sequence segment generates a secondresonant signal in the second shell. In various embodiments, the firstresonant signal and the second resonant signal are detected and used todetermine NMR properties for the substance (e.g., T₁, T₂, or diffusion).In some embodiments, such properties can be determined for the firstshell of the substance based upon the first resonant signal and thesecond shell of the substance based upon the second resonant signal.

In further exemplary embodiments, the NMR pulse sequence includes atleast three pulse sequence segments that are applied at differentfrequencies and configured to generate resonant signals in threedifferent shells of the substance (e.g., 4, 5, or 9 sequence segments).

Illustrative embodiments of the present disclosure are also directed toa system for applying an NMR pulse sequence. The system includes a coilfor applying the pulse sequence to a substance and a NMR transmitterthat includes non-resonant transmitter circuit. The non-resonanttransmitter circuit is electronically coupled to the coil. The systemfurther includes a processor and a memory that stores instructionsexecutable by the processor to perform processes. These processesinclude providing the NMR pulse sequence to the NMR transmitter. The NMRpulse sequence includes a first pulse sequence at a first frequency forapplication to a first shell and a second pulse sequence at a secondfrequency for application to a second shell. The second pulse sequencesegment is configured to be applied before the first shell reachesthermal equilibrium.

Illustrative embodiments of the present disclosure are also directed toa method for applying a NMR sequence with interposed segments. Themethod includes applying an NMR pulse sequence to the substance using acoil. The NMR pulse sequence includes at least a first pulse sequencesegment at a first frequency applied to a first shell and a second pulsesequence segment at a second frequency applied to a second shell. Thesecond pulse sequence segment is interposed within the first pulsesequence segment.

Furthermore, illustrative embodiments of the present disclosure aredirected to a method for applying an NMR sequence to different atomicnuclei within a substance. The method includes applying a staticmagnetic field to the substance and applying an NMR pulse sequence tothe substance using a non-resonant transmitter circuit. The NMR pulsesequence includes a first pulse sequence segment applied at a firstfrequency to a first set of atomic nuclei and a second pulse sequencesegment applied at a second frequency to a second set of atomic nuclei.The first set of atomic nuclei and the second set of atomic nuclei aredifferent chemical sets of atomic nuclei. In some embodiments, thesecond pulse sequence segment is initiated before the first set ofatomic nuclei reach thermal equilibrium. In yet another specificembodiment, the first pulse sequence segment and second pulse sequencesegment are interposed.

Illustrative embodiments of the present disclosure are also directed toa system for applying an NMR sequence to different atomic nuclei withina substance. The system includes a coil for applying the pulse sequenceto a substance and a NMR transmitter that includes a non-resonanttransmitter circuit. The non-resonant transmitter circuit iselectronically coupled to the coil. The system further includes aprocessor and a memory for storing instructions executable by theprocessor to perform processes. The processes include providing the NMRpulse sequence to the NMR transmitter. The NMR pulse sequence includes afirst pulse sequence segment for application at a first frequency to afirst set of atomic nuclei and a second pulse sequence segment forapplication at a second frequency to a second set of atomic nuclei. Thefirst set of atomic nuclei and the second set of atomic nuclei aredifferent chemical sets of nuclei.

BRIEF DESCRIPTION OF THE DRAWINGS

Further features and advantages will become more readily apparent fromthe following detailed description when taken in conjunction with theaccompanying drawings:

FIG. 1 shows a method of applying an NMR pulse sequence in accordancewith one embodiment of the present disclosure;

FIG. 2 shows an NMR pulse sequence with multiple pulse sequence segmentsin accordance with one embodiment of the present disclosure;

FIG. 3 shows an area of interest within a substance in accordance withone embodiment of the present disclosure;

FIG. 4 shows an NMR pulse sequence with multiple pulse sequence segmentsin accordance with another embodiment of the present disclosure;

FIG. 5 shows four shells generated by a four-segment NMR pulse sequencein accordance with another embodiment of the present disclosure;

FIG. 6 shows interleaved shells in accordance with one embodiment of thepresent disclosure;

FIG. 7 shows a plot of summed echo amplitude versus time in accordancewith one embodiment of the present disclosure;

FIG. 8 shows a plot of normalized amplitude versus delay time inaccordance with one embodiment of the present disclosure;

FIG. 9 shows a plot of echo amplitude versus diffusion weighting inaccordance with one embodiment of the present disclosure;

FIG. 10 shows a plot of relative echo amplitude versus frequency offsetin accordance with one embodiment of the present disclosure;

FIG. 11 shows a pulse with a Gaussian envelope as compared with arectangular pulse in accordance with one embodiment of the presentdisclosure;

FIG. 12 shows an NMR pulse sequence with interposed pulse sequencesegments in accordance with one embodiment of the present disclosure;

FIG. 13 shows an area of interest within a substance in accordance withone embodiment of the present disclosure;

FIG. 14 shows an NMR pulse sequence with interposed pulse sequencesegments in accordance with another embodiment of the presentdisclosure;

FIG. 15 shows three shells generated by a three-segment NMR pulsesequence within an area of interest of a substance in accordance withone embodiment of the present disclosure;

FIG. 16 shows an NMR pulse sequence with greater than two interposedpulse sequence segments in accordance with one embodiment of the presentdisclosure;

FIG. 17 shows a plot of signal amplitude versus time in accordance withone embodiment of the present disclosure;

FIG. 18 shows a multi-segment sequence for determining T1 relaxationtime in accordance with one embodiment of the present disclosure;

FIG. 19 shows a simulated plot of asymptotic echo amplitude versus echoacquisition time in accordance with one embodiment of the presentdisclosure;

FIG. 20 shows a measured plot of asymptotic echo amplitude versus echoacquisition time in accordance with one embodiment of the presentdisclosure;

FIG. 21 shows a multi-segment sequence for determining an appliedoscillating field (B₁) in accordance with one embodiment of the presentdisclosure;

FIG. 22 shows a multi-segment sequence for determining an appliedoscillating field (B₁) in accordance with another embodiment of thepresent disclosure;

FIG. 23 shows a multi-segment sequence for determining an appliedoscillating field (B₁) in accordance with yet another embodiment of thepresent disclosure;

FIG. 24 shows an effective on-resonance magnetic field in a rotatingframe of an off-resonant pulse in accordance with yet another embodimentof the present disclosure;

FIG. 25 shows a plot of amplitude of asymptotic echoes as a function ofvarious on-resonant pulse lengths (T) and two values of off-resonantpulse lengths (T_(BS)) in accordance with one embodiment of the presentdisclosure;

FIG. 26 shows a plot of amplitude of asymptotic echoes as a function ofvarious on-resonant pulse lengths (T) and two values of off-resonantpulse lengths (T_(BS)) in accordance with one embodiment of the presentdisclosure;

FIG. 27 shows a plot of measured B-S phase shift for a doped-watersample for various off-resonant pulse lengths (T_(BS)) in accordancewith one embodiment of the present disclosure;

FIG. 28 shows a plot of normalized echo amplitude as a function ofexcitation pulse length in accordance with one embodiment of the presentdisclosure;

FIG. 29 shows a plot of measured asymptotic CPMG echoes for a sodiumsample in accordance with one embodiment of the present disclosure;

FIG. 30 shows a plot of measured asymptotic CPMG echoes for a deuteriumsample in accordance with one embodiment of the present disclosure;

FIG. 31 shows a plot of measured proton and sodium depth profiles for abrine sample in accordance with one embodiment of the presentdisclosure;

FIG. 32A shows a broadband NMR device in accordance with one embodimentof the present disclosure;

FIG. 32B shows a non-resonant NMR transmitter circuit in accordance withone embodiment of the present disclosure;

FIG. 32C shows a broadband NMR receiver in accordance with oneembodiment of the present disclosure;

FIG. 32D shows a preamplifier in accordance with one embodiment of thepresent disclosure;

FIG. 32E shows a preamplifier in accordance with another embodiment ofthe present disclosure;

FIG. 33 shows a broadband NMR system for applying multi-segmentsequences to a substance in accordance with one embodiment of thepresent disclosure;

FIG. 34 shows a wireline system for applying multi-segment sequences toa substance in accordance with one embodiment of the present disclosure;

FIG. 35 shows another wireline system for applying multi-segmentsequences to a substance in accordance with one embodiment of thepresent disclosure;

FIG. 36 shows a logging-while-drilling (LWD) system for applyingmulti-segment sequences to a substance in accordance with one embodimentof the present disclosure; and

FIG. 37 shows an LWD NMR logging module for applying multi-segmentsequences to a substance in accordance with one embodiment of thepresent disclosure.

DETAILED DESCRIPTION

Illustrative embodiments of the present disclosure are directed tosystems and methods for applying a nuclear magnetic resonance (NMR)sequence to a substance that improve the efficiency of NMR measurements.To this end, various embodiments apply an NMR pulse sequence withmultiple pulse sequence segments. The multi-segment sequence includes atleast a first pulse sequence segment and a second pulse sequencesegment. The pulse sequence segments are applied to the substance atdifferent frequencies and generate resonant signals in a first shell anda second shell within the substance. The second pulse sequence segmentis initiated before the first shell reaches thermal equilibrium. In thismanner, various embodiments of the present disclosure reduce idle time,whereas in many conventional systems, a second NMR sequence segment isnot initiated until the first shell reaches thermal equilibrium. SuchNMR pulse sequence with multiple pulse sequence segments can also beapplied to different atomic nuclei. Details of various embodiments arediscussed below.

FIG. 1 shows a method 100 of applying an NMR pulse sequence withmultiple segments in accordance with one embodiment of the presentdisclosure. The method 100 includes applying a static magnetic field(B₀) to an area of interest within a substance 102, such as a reservoirformation containing hydrocarbons. In some embodiments, an inhomogeneousmagnetic field is applied to the substance. The term “inhomogeneous”should be considered in the context of the NMR art. Many NMR welllogging tools deploy inhomogeneous static magnetic fields due to thelimitations and constraints of a borehole environment. In this context,an inhomogeneous static magnetic field is a static magnetic field thatvaries in intensity or direction within an area of interest of thesubstance. In one example, an inhomogeneous static magnetic field withina shell may vary in intensity by a value approximately equal to orgreater than a nominal RF magnetic field (B₁) amplitude of an NMR pulsesequence applied to the area of interest. The inhomogeneous static fieldvariation within a shell will be proportional to the intensity of B₁.For example, with rectangular pulses the variation is approximately 2B₁.As B₁ increases the shell becomes thicker, so more variation in thestatic field occurs within the shell.

Once the static magnetic field is applied to the area of interest, themethod includes applying an NMR pulse sequence to the area of interestwithin the substance 104. In some embodiments, the NMR pulse sequence isa series of radio frequency (RF) pulses. FIG. 2 shows an NMR pulsesequence 200 with multiple pulse sequence segments in accordance withone embodiment of the present disclosure. The NMR pulse sequence 200includes at least a first pulse sequence segment 202 and a second pulsesequence segment 204. Each segment includes an excitation pulse 206, aseries of refocusing pulses 208, and a series of echoes 210. In variousembodiments, the excitation pulses have a length of T₉₀ and therefocusing pulses have a length of T₁₈₀. T₉₀ is defined as:T₉₀=π/2(γ×B₁), where γ is the gyromagnetic ratio of a nucleus ofinterest and B₁ is the maximum amplitude of an appliedcircularly-polarized magnetic field in a rotating frame within the areaof interest within the substance (e.g., in many cases, B₁ is half theamplitude of the linearly-polarized magnetic field produced by a coil).T₁₈₀ is defined as: T₁₈₀=π/(γ×B₁). The pulses also have amplitudes thattypically range between 1 G (Gauss) and 10 G. In one specific example,the sequence segments 202, 204 are Carr, Purcell, Meiboom and Gill(CPMG) sequences. In various other embodiments, the sequence segments202, 204 can be spin echo, inversion recovery, saturation recovery,and/or stimulated echo sequences. Illustrative embodiments of thepresent disclosure, however, are not limited to such specific sequences,pulse lengths, and amplitudes.

As shown in FIG. 2, the first segment 202 is applied to the substance ata first set of frequencies (ω_(RF1)) and the second segment 204 isapplied to the substance at a second set of frequencies (ω_(RF2)). Anaverage of the first set of frequencies and an average of the secondfrequencies are different by a value of Δω_(RF). In some embodiments,the frequency difference (Δω_(RF)) is as great as 10% of the average ofthe first set of frequencies. In various other embodiments, thefrequency difference can be even greater (e.g., 20%, 30%, or 50%). In aspecific example, the frequency of a first pulse segment isapproximately 1 MHz and the next segment is applied at 0.5 MHz or 0.75MHz (e.g., Δω_(RF)/2π=0.5 MHz or 0.25 MHz). In another specific example,the frequency difference is sufficient to switch between the resonantfrequencies of hydrogen nuclei (¹H, or protons) and sodium nuclei(²³Na). The hydrogen nuclei and sodium nuclei can be different by asmuch as a factor of four.

The term “set” of frequencies is used because the frequency within apulse segment or a single pulse may not be a single frequency. Thefrequency within a pulse sequence segment or a single pulse can varyover a set of frequencies (e.g., over a range of frequencies). In someembodiments, the frequency may be specifically selected to vary within apulse sequence segment or a single pulse. Furthermore, resonant signalsgenerated within a shell can also vary over a set of frequencies.Reference within the present disclosure to a specific frequency shouldnot be interpreted as limited to that specific frequency because thatfrequency may vary within a pulse sequence segment or even a singlepulse.

The NMR pulse sequence 200 applied to the substance generates resonantsignals within the substance. The resonant signals are composed of aseries of echoes. The first pulse sequence segment 202 will generate afirst resonant signal in a first shell, while the second pulse sequencesegment 204 will create a second resonant signal within a second shell.A “shell” is a region of the substance that produces a resonant signalin response to an NMR pulse sequence applied with a particular set offrequencies. In a homogenous static magnetic field, the shell will bebroad across an area of interest within the substance because the field(B₀) is constant. In an inhomogeneous static magnetic field, the fieldchanges across the area of interest and NMR pulse sequences at aparticular frequency produce resonant signals in a limited region withinarea of interest. This limited region is referred to herein as a “shell”or a “slice.”

FIG. 3 shows an area of interest 300 within a substance 302 inaccordance with one embodiment of the present disclosure. In FIG. 3, aninhomogeneous magnetic field 304 is applied to the area of interest 300within the substance 302. When the first pulse sequence segment 202 andthe second pulse sequence segment 204 are applied to the area ofinterest 300 within the substance 302, the substance generates tworesonant signals with two different frequencies (e.g., sets offrequencies). The first resonant signal originates at a first shell 306and a second resonant signal originates at a second shell 308 within thearea of interest 300. The two resonant signals have differentfrequencies because the static magnetic field 304 is different at eachlocation within the area of interest 300 of the substance 302. Thefrequency of each signal can be determined using the following equation:

ω₀ =γ×B ₀  Eq. 1

where B₀ is the strength of the static magnetic field 304, γ is thegyromagnetic ratio of the atomic nuclei of interest, and ω₀ is thefrequency of the resonant signal that is produced by the atomic nuclei.The frequency of the resonant signals is also known as the Larmorfrequency. For a hydrogen nucleus, the gyromagnetic ratio is 4258Hz/Gauss. Given the relationship defined in Equation 1, if a staticmagnetic field of 235 Gauss is applied to the nucleus, the frequency ofthe resulting signal would be 1 MHz.

NMR pulse sequences are typically applied a number of times to a singleshell within the substance (e.g., N=10, N=100, or N=1000) to improve theaccuracy of the measurement. Conventional NMR systems typically do notapply a second NMR pulse sequence to the shell immediately after a firstNMR pulse sequence. Instead, conventional systems sit idle until theshell reaches thermal equilibrium. Conventional wisdom suggests thatapplying a second NMR sequence before the shell reaches thermalequilibrium may produce inaccuracies in the second measurement. In somecases, conventional systems sit idle for several T₁ time constantsbefore resuming application of NMR sequences. For example, if thesubstance of interest includes light oil, the idle time can be as greatas 10 seconds. This idle time increases measurement time, which iscostly in NMR borehole logging applications and also decreases the SNRavailable per unit time.

Illustrative embodiments of the present disclosure initiate the secondpulse sequence segment 204 before the first shell 306 reaches thermalequilibrium. In this manner, various embodiments speed up NMRmeasurements and improve SNR. As shown in FIG. 2, the first pulsesequence segment 202 includes a refocusing pulse 208 and a correspondingecho 210 that are repeated a number of times (e.g., N_(E)=10, N_(E)=100,N_(E)=1000) to form a series (e.g., train) of refocusing pulses andcorresponding echoes. Once the first pulse sequence segment 202 iscomplete, the first shell 306 will reach a point of thermal equilibrium212 during a time period 214. Before this point of thermal equilibrium212, the second pulse sequence 204 segment is initiated and applied tothe second shell 308. The term “thermal equilibrium” should beconsidered in the context of the NMR art. Many NMR logging tools do notapply a subsequent pulse sequence to a shell until most of the nuclei ofinterest within the shell are aligned with the initial magnetizationinduced by the static magnetic field. The approach to thermalequilibrium is exponential. The approach can be written asM(t)=M(0)e^(−t/T1)+M(∞)(1−e^(−t/T1)), where M(0) and M(∞) are theinitial magnetization and thermal equilibrium magnetization,respectively, and t=0 corresponds to the end of the first pulse sequencesegment 202. For practical purposes this infinitely long process isassumed to have completed once the term e^(−t/T1) becomes very small(e.g., t is much greater than T₁). In one example, a shell is assumed toreach thermal equilibrium over a time period (e.g., 214) that is fivetimes T₁, resulting in e^(−t/T1)=0.00674. The time period begins whenthe prior pulse sequence (e.g., 202) is completed. In another specificexample, the time period (e.g., 214) is less than five times T₁ (e.g.,four times T₁).

In accordance with the method 100 shown in FIG. 1, the first resonantsignal generated at the first shell 306 and/or the second resonantsignal generated at the second shell 308 are detected. These detectedsignals can be used to determine NMR properties for the substance 302(e.g., T₁ relaxation time, T₂ relaxation time, diffusion, and/or acorrelation function of such properties). In turn, the NMR propertiescan be used to determine physical properties of the substance, such asthe chemical composition of the substance and/or the presence of a solidphase, a liquid phase, and/or a gas phase within the substance.

FIG. 4 shows an NMR pulse sequence 400 with multiple pulse sequencesegments in accordance with another embodiment of the presentdisclosure. In FIG. 4, the NMR pulse sequence 400 includes four pulsesequence segments. A first segment 402 is applied to the substance witha first set of frequencies (ω_(RF1)), a second segment 404 is applied tothe substance with a second set of frequencies (ω_(RF2)), a thirdsegment 406 is applied to the substance with a third set of frequencies(ω_(RF3)), and a fourth segment 408 is applied to the substance with afourth set of frequencies (ω_(RF4)). These frequencies are substantiallysimilar to the average Larmor frequency of each shell in order tosatisfy the resonance condition (ω₀=ω_(RF)) within each shell. FIG. 5shows four shells 504, 506, 508, 510 generated by the four-segment NMRpulse sequence 400 within an area of interest 500 of the substance 502.In this case, an inhomogeneous static magnetic field is applied to thearea of interest 500.

As shown in FIG. 4, the second segment 404 is initiated before the firstshell 504 reaches a point of thermal equilibrium 410. The third segment406 is initiated before the second shell 506 reaches a point of thermalequilibrium 412. The fourth segment 408 is initiated before the thirdshell 508 reaches a point of thermal equilibrium 414. At this point, insome embodiments, the NMR measurement stops. In various otherembodiments, the NMR pulse sequence is repeated a number of times (N)and the first segment 402 is initiated before the fourth shell 510reaches a point of thermal equilibrium 416.

Illustrative embodiments of the present disclosure are not limited totwo, three or four pulse sequence segments. Exemplary embodiments of theNMR pulse sequences may include five, six, nine, or more such pulsesequence segments.

Illustrative embodiments of the present disclosure are also directed tomethods for avoiding interaction between shells because interactionsbetween shells can produce inaccuracies in the measurement. In one suchembodiment, NMR pulse sequence segments are interleaved to avoidinteraction between shells. An NMR pulse sequence is interleaved when atleast some of the shells are temporally skipped to avoid interactionwith adjacent shells. FIG. 6 shows interleaved shells in accordance withone embodiment of the present disclosure. In this case, an NMR pulsesequence is applied to an area of interest 600 within a substance 602.The NMR sequence includes six pulse sequence segments applied at sixdifferent frequencies (ω_(RF1), ω_(RF2), ω_(RF3), ω_(RF4), ω_(RF5) andω_(RF6)). The six pulse sequence segments generate six shells 604, 606,608, 610, 612, 614 within the area of interest 600. Instead of applyingthe pulse sequence segments in order of increasing frequency (e.g.,ω_(RF1), 604→ω_(RF2), 606→ω_(RF3), 608→ω_(RF4), 610→ω_(RF5),612→ω_(RF6), 614) or decreasing frequency (e.g., ω_(RF6), 614→ω_(RF5),612→ω_(RF4), 610→ω_(RF3), 608→ω_(RF2), 606→ω_(RF1), 604), the shells aretemporally skipped to avoid interaction with adjacent shells. The shellsthat are skipped are then analyzed at a later time. The following is anon-limiting list of interleaved pulse sequence segments:

-   -   ω_(RF1), 604→ω_(RF3), 608→ω_(RF5), 612→ω_(RF2), 606→ω_(RF4),        610→ω_(RF6), 614    -   ω_(RF2), 606→ω_(RF4), 610→ω_(RF6), 614→ω_(RF1), 604→ω_(RF3),        608→ω_(RF5), 612    -   ω_(RF1), 604→ω_(RF6), 614→ω_(RF2), 606→ω_(RF4), 610→ω_(RF3),        608→ω_(RF5), 612

In this manner, pulse sequence segments can be interleaved to avoidinteraction with adjacent shells.

In illustrative embodiments of the present disclosure, NMR pulsesequences are applied to a substance using an NMR system. In someembodiments, the NMR system may include a single coil. Also, theresonant signals generated by the NMR sequences are detected by thecoil. In additional or alternative embodiments, the NMR system includesone coil for applying NMR pulse sequences and another coil for detectingresonant signals. In various embodiments, the NMR system includesbroadband NMR electronics that are coupled to the coil. The broadbandelectronics are configured to transmit an NMR pulse sequence to the coiland/or to receive resonant signals that are detected by the coil.Further details of broadband NMR electronics are shown in FIGS. 32A,32B, 32C, 32D, and 32E.

In various embodiments of the present disclosure, the detected resonantsignals that are received by the broadband electronics can be used todetermine various properties of the substance, such as an NMR propertyfor the substance. The NMR property can be one or more of T₁ relaxationtime, T₂ relaxation time, diffusion, and/or correlation function of suchproperties.

In some embodiments, one or more properties can be determined for eachof the shells based on the resonant signals originating at therespective shell. In this manner, a depth profile can be determined forthe substance. For example, in FIG. 6, the T₁ relaxation time for eachshell 604, 606, 608, 610, 612, 614 can be determined. Such a profileprovides information about how the properties of the substance arechanging over the area of interest 600 along a depth dimension 616. Insuch exemplary embodiments, the multi-segment sequences advantageouslyspeed up measurement of the depth profile by initiating the next pulsesequence before the prior shell reaches thermal equilibrium.

In additional or alternative embodiments, the resonant signals from aplurality of shells (N_(S)) are combined. For example, the amplitudes ofeach resonant signal can be added together. In some cases, the resonantsignals add coherently across the shells, while the noise addsincoherently. The combined signal is used to differentiate the actualresonant signal from noise. In this manner, the combination of signalsimproves the signal to noise ratio (SNR). According to one exemplarymeasure, SNR increases by a factor of the square root of the number ofpulse sequence segments (√{square root over (N_(S))}). In this manner,illustrative embodiments of the present disclosure improve SNR for NMRmeasurements.

FIG. 7 shows a plot 700 of summed echo amplitude versus time inaccordance with one embodiment of the present disclosure. Morespecifically, the plot shows a summed amplitude for an NMR pulsesequence with four pulse sequence segments at four different shells(e.g., N_(S)=4) as compared with an NMR pulse sequence at a singleshell. The top curve 702 is the sum of the four-shell sequence, thesecond curve 704 is the single-shell sequence, and the lower curves 706are noise channels. The SNR for the four-segment sequence 702 was 303,while the SNR for the single-shell sequence 704 was 190. The NMRsequences were applied to a doped-water sample. The doped-water samplehad a T₂ relaxation time of 120 ms. The NMR pulse sequences were appliedto the sample using broadband NMR electronics, as described furtherbelow. Within the four-segment sequence, the first segment was appliedat 2.0 MHz (e.g., ω_(RF)/2π=2.0 MHz) and the frequency differencebetween the segments was 10 kHz (e.g., Δω_(RF)/2π=10 kHz=5.6 ω₁). Also,the excitation pulses for each segment had a duration of 140 μs (e.g.,T₉₀=140 μs). The echo spacing within each shell was 800 μs (e.g.,T_(E)=800 μs) and the four-segment sequence was repeated four times(e.g., N=4). The SNR for the four-segment sequence was greatly improvedeven though the total time for applying the four-segment sequence wasapproximately equal to the total time for applying the one-shellsequence. This is so because, in the one-shell sequence, there was anidle time of 500 ms between repetitions of the sequence (e.g., wait timeT_(W)=500 ms), whereas, there was no idle time between repetitions ofthe four-segment sequence (e.g., T_(W)=0 ms).

In yet another embodiment of the present disclosure, multi-segmentsequences are applied in 2D NMR measurements. In one exemplaryembodiment, each different shell number (e.g., N_(S)) of a multi-segmentsequence is used as an indirect dimension (e.g., second dimension). Inother words, each shell can be encoded with a different value of anindirect variable, such as a delay between two pulses in the pulsesequence. In this manner, illustrative embodiments of multi-shellsequences speed up 2D NMR measurements (e.g., diffusion and T₁relaxation time) because at least some of the wait times between thesequences can be nullified. The speed up factor can be determined by:

$\begin{matrix}{S = {1 + \frac{T_{W}}{N_{E}T_{E}}}} & {{Eq}.\mspace{14mu} 2}\end{matrix}$

Where T_(W) is the wait time between pulse sequence segments, N_(E) isthe number of refocusing pulses and corresponding echoes within eachpulse sequence segment, and T_(E) is the echo spacing. In someembodiments, T_(W) is approximately equal to 3 times T₁ to allow forlongitudinal relaxation of the shell. Also, in some embodimentsN_(E)T_(E) is approximately equal to 1.26 times T₂ to maximize SNR.Given the relationship defined in Equation 2, the speed up factor can bedetermined by:

$\begin{matrix}{S \approx {1 + {2.4\frac{T_{1}}{T_{2}}}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

FIG. 8 shows a plot 800 of normalized amplitude versus delay time inaccordance with one embodiment of the present disclosure. Morespecifically, the plot shows normalized amplitude for a 2D NMRmeasurement. The measurement used an inversion recovery sequence formeasuring T₁ that was accelerated by encoding each shell with adifferent recovery time. Also, the measurement used a multi-segmentsequence with six pulse sequence segments at six different shells (e.g.,N_(S)=6). The pulse sequence segments were interleaved to reduceinteraction between shells. The pulse sequence segments were interleavedin the following manner:ω_(RF1),→ω_(RF3),→ω_(RF5),→ω_(RF2),→ω_(RF4),→ω_(RF6). The sequence hadno idle time between segments.

The 2D NMR measurement was applied to a doped-water sample. Thedoped-water sample had a T₂ relaxation time of 120 ms. The NMR pulsesequences were applied to the sample using broadband NMR electronics.The first pulse sequence segment was applied at 1.25 MHz (e.g.,ω_(RF)/2π=1.25 MHz) and the frequency difference between the pulsesequence segments was 13 kHz (e.g., Δω_(RF)/2π=13 kHz=4.4 ω₁). Also, theexcitation pulses for each segment had a duration of 90 μs (e.g., T₉₀=90μs). The echo spacing within each shell was 1 ms (e.g., T_(E)=1 ms) andthe pulse sequence were repeated 128 times (e.g., N=128). The 2D NMRmeasurement determines the value of T₁ from decay data, as shown in forexample FIG. 8. In this example, T₁ is equal to 125 ms.

FIG. 9 shows a plot 900 of echo amplitude versus diffusion weighting inaccordance with one embodiment of the present disclosure. Morespecifically, the plot shows echo amplitude for another 2D NMRmeasurement at three different locations within a sample. Themeasurement used a low-gradient diffusion editing (LG-DE) sequence formeasuring a molecular diffusion coefficient. The LG-DE sequence wasaccelerated by encoding each shell with a different diffusion time. Themeasurement used a multi-segment sequence with six pulse sequencesegments at six different shells (e.g., N_(S)=6). The pulse sequencesegments were also interleaved in the following manner:ω_(RF),→ω_(RF3),→ω_(RF5),→ω_(RF2),→ω_(RF4),→ω_(RF6). In this case, thesequence had an idle time of 5 ms between segments. Such a small delaycan reduce artifacts in the decay curve by ensuring that diffusionnullifies at least a portion of the transverse magnetization before thenext shell is excited. During the measurement, a dummy shell (e.g.,separated from the first shell by the normal shell separation) wasexcited before the first shell was excited. A dummy shell furtherreduces artifacts in the decay curve by ensuring that all shells areequally spoiled by preceding excitations.

The 2D NMR measurement was applied to a doped-water sample at threedifferent sample locations. The doped-water sample had a T₂ relaxationtime of 120 ms. The NMR pulse sequences were applied to the sample usingbroadband NMR electronics. The first pulse sequence segments wereapplied at the following frequencies: 1.51 MHz; 1.30 MHz; 1.01 MHz(e.g., ω_(RF)/2π=1.51 MHz; ω_(RF)/2π=1.30 MHz; ω_(RF)/2π=1.01 MHz). Thefrequency difference between the pulse sequence segments was 10 kHz(e.g., Δω_(RF)/2π=10 kHz). Also, the excitation pulses for each segmentat the three different locations had a duration of 105 μs, 87.5 μs, and70 μs (e.g., T₉₀=105 μs; T₉₀=87.5 μs; T₉₀=70 μs). The echo spacingwithin each shell was 1 ms (e.g., T_(E)=1 ms) and the pulse sequence wasrepeated 128 times (e.g., N=128). As shown in FIG. 9, the 2D NMRmeasurement determines a correct value for a diffusion coefficient (D).The figure also shows that the measurements are independent of thenominal Larmor frequency of the sample (e.g., the location of themeasurement within the sample). Further measurements demonstratedsimilar favorable results for more widely-separated locations within thesample.

FIG. 10 shows a plot 1000 of relative echo amplitude versus frequencyoffset in accordance with one embodiment of the present disclosure. Morespecifically, the plot shows measured “spoiling” between nearby shellsfor rectangular pulses as a function of the frequency offset. Thethickness of a shell is defined at least in part by the longitudinalmagnetization of the nuclei within the shell. When applying NMRsequences, in many cases, it is much easier to nullify longitudinalmagnetization than to generate the required transverse magnetization.For this reason, common pulse sequences, such as CPMG sequences, create“holes” in longitudinal magnetization that are much wider than theshells from which they produce detectable resonant signals. Such “holeburning” or “spoiling” limits the minimum spacing between adjacentshells. The plot in FIG. 10 shows measured “spoiling” between nearbyshells for rectangular pulses as a function of the frequency offset. Themeasurement was performed using a series of CPMG sequences applied atdifferent offset frequency values (e.g., Δω_(RF)). The measurement wasapplied to a doped-water sample having a T₂ relaxation time of 120 ms.Furthermore, the pulse sequences were applied to the sample usingbroadband NMR electronics. FIG. 10 shows that a frequency offset Δω₀between shells of greater than four times ω₁ provides for less than 10%spoiling, where ω₁=γB₁. Also, there is very little spoiling forfrequency offset values Δω₀ that are greater than 8 times ω₁. For 90degree rectangular pulses and 180 degree rectangular pulses zerospoiling occurs when the resonant offset frequency has the valuesdetermined by Equation 4 and Equation 5, respectively:

Δω₀=±(√{square root over (16n ²−1))}ω₁  Eq. 4

Δω₀=±(√{square root over (4n ²−1))}ω₁  Eq. 5

where n is an integer (e.g., 1, 2, . . . ).

In illustrative embodiments of the present disclosure, such interactionsbetween shells can be reduced by using shaped pulses that gradually turnon and off. In one such example, pulses with Gaussian envelopes reducethe amount of spoiling and hole burning between shells. FIG. 11 shows apulse with a Gaussian envelope 1100 as compared with a rectangular pulse1102 in accordance with one embodiment of the present disclosure. Inthis manner, illustrative embodiments reduce interactions betweenshells.

Illustrative embodiments of the present disclosure are directed tomulti-segment sequences that further improve the efficiency of NMRmeasurements (e.g., interposed sequences). To this end, variousembodiments apply at least two pulse sequence segments to a substance.The NMR pulse sequence segments are applied at two different frequenciesand are interposed within each other. In this manner, such variousinterposed sequences perform measurements in parallel, whereas in manyconventional systems, the measurements are performed in series.

FIG. 12 shows an NMR pulse sequence 1200 with interposed pulse sequencesegments in accordance with one embodiment of the present disclosure.The NMR pulse sequence 1200 includes at least a first pulse sequencesegment 1202 and a second pulse sequence segment 1204. Each segmentincludes an excitation pulse 1206, a series of refocusing pulses 1208,and a series of echoes 1210. In various embodiments, the excitationpulses have a length of T₉₀ and the refocusing pulses have a length ofT₁₈₀. The pulses also have amplitudes that typically range between 1 Gand 10 G. In one specific example, the sequence segments 1202, 1204 areCPMG sequences. In various other embodiments, the sequence segments 202,204 can be spin echo, inversion recovery, saturation recovery, and/orstimulated echo sequences. Illustrative embodiments of the presentdisclosure, however, are not limited to such specific sequences, pulselengths and amplitudes.

As shown in FIG. 12, the second segment 1204 is interposed within thefirst segment 1202. In other words, at least one pulse or detected echoof the second sequence segment 1204 occurs before the first pulsesequence segment 1202 is completed. The first segment 1202 is applied tothe substance with a first set of frequencies (ω_(RF1)) and the secondsegment 1204 is applied to the substance with a second set offrequencies (ω_(RF2)). An average of the first set of frequencies and anaverage a second set of frequencies are different by a difference ofΔω_(RF). In some embodiments, the frequency difference of Δω_(RF) is asgreat as 10% of the first frequency. In various other embodiments, thefrequency can be even greater (e.g., 20% 30% or 50%).

The NMR pulse sequence 1200 applied to the substance generates resonantsignals within the substance. The resonant signals are composed of aseries of echoes. The first pulse sequence segment 1202 will generate afirst resonant signal in a first shell, while the second pulse sequencesegment 1204 will create a second resonant signal within a second shell.

FIG. 13 shows an area of interest 1300 within a substance 1302 inaccordance with one embodiment of the present disclosure. In FIG. 13, aninhomogeneous magnetic field 1304 is applied to the area of interest1300 within the substance 1302. When the first pulse sequence segment1202 and the second pulse sequence segment 1204 are applied to the areaof interest 1300 within the substance 1302, the substance generates tworesonant signals with two different frequencies (e.g., sets offrequencies). The first resonant signal originates at a first shell 1306and a second resonant signal originates at a second shell 1308 withinthe area of interest 1300. The two resonant signals have differentfrequencies because the static magnetic field 1304 is different at eachlocation within the area of interest 1300 of the substance 1302. Thefrequency of each signal can be determined using, for example, Equation1, where B₀ is the strength of the static magnetic field 1304, γ is thegyromagnetic ratio of the atomic nuclei of interest and ω₀ is thefrequency of the resonant signal that is produced by the atomic nuclei.

The first resonant signal and the second resonant signal are detected.These detected signals can be used to determine NMR properties for thesubstance 1302 (e.g., T₁ relaxation time, T₂ relaxation time and/ordiffusion). In turn, the NMR properties can be used to determinephysical properties of the substance, such as the chemical compositionof the substance and/or the presence of solid phase and/or liquid phasewithin the substance.

FIG. 14 shows an NMR pulse sequence 1400 with interposed pulse sequencesegments in accordance with another embodiment of the presentdisclosure. In FIG. 14, the NMR pulse sequence 1400 includes three pulsesequence segments. A first segment 1402 is applied to the substance witha first set of frequencies (ω_(RF1)), a second segment 1404 is appliedto the substance with a second set of frequencies (ω_(RF2)), and a thirdsegment 1406 is applied to the substance with a third set of frequencies(ω_(RF3)). Each of the second segment 1404 and the third segment 1406are interposed within the first segment 1402. Such an NMR pulse sequence1400 generates resonant signals within three shells. FIG. 15 shows threeshells 1504, 1506, 1508 generated by the three-segment NMR pulsesequence 1400 within an area of interest 1500 of the substance 1502.Illustrative embodiments of the present disclosure are not limited totwo or three interposed pulse sequence segments. Exemplary embodimentsmay include 4, 5, 9 or more interposed pulse sequence segments.

FIG. 16 shows an NMR pulse sequence 1600 with greater than twointerposed pulse sequence segments in accordance with one embodiment ofthe present disclosure. The NMR pulse sequence 1600 includes a number ofpulse sequence segments (N_(S)). Each segment includes an excitationpulse 1602, a series of refocusing pulses 1604, and a series of echoes1606. The sequence segments are applied to the substance with differentfrequencies. In the specific example shown in FIG. 16, the frequency ofthe n-th segment is given by ω_(RF)+(n−1)Δω_(RF), where Δω_(RF) is theseparation between adjacent shells and 1≦n≦N_(S). In various otherembodiments, the separation between shells is not constant and varies.

Also, in one specific embodiment, the refocusing pulse lengths anddelays between refocusing pulses can be set to integer multiples of1/(Δω_(RF)) to maintain phase coherence within each shell. In additionalor alternative embodiments, phase coherence can be maintained byexplicitly tracking the phase of each shell in a rotating frame andappropriately modulating the phase of the refocusing pulses.

As shown in FIG. 16, echoes from each shell form sequentially in time(e.g., separated by T_(S), where T_(S) is the length of each refocusinginterval and excitation interval). Given this phenomenon, the echoes canbe distinguished from each other based upon their placement in time. Inadditional or alternative embodiments, the echoes can be distinguishedfrom each other based upon their frequency content.

Illustrative embodiments of the present disclosure are also directed tocompensating for the Bloch-Siegert (B-S) phase shift. The inventorsherein have discovered that interposed pulse sequence segments withdifferent frequencies can be adversely affected by the B-S phase shift.In particular, the B-S phase shift can cause rapid signal decay whenapplying an NMR pulse sequence with interposed pulse sequence segments.To prevent this rapid signal decay, the B-S phase shift can be correctedby phase shifting excitation pulses for the second and successive pulsesequence segment (e.g., N_(S)>1). In other words, each excitation pulseapplied subsequent to the first excitation pulse is applied with ashifted phase. In an additional or alternative embodiment, the timeinterval between each excitation pulse is varied to account for the B-Sshift within a single shell. Details of these corrections are providedbelow.

In various embodiments, the timing of a pulse sequence segment isadjusted such that the phase acquired between the excitation pulse andthe first refocusing pulse is about half the phase acquired in eachrefocusing cycle. In some embodiments, this phase is proportional to theLarmor frequency and can be determined by:

φ_(L)=γω_(RF) T _(E)  Eq. 6

where γ is the gyromagnetic ratio of a nucleus of interest, N_(RF) isthe frequency of the pulse sequence segment, and T_(E) is the echospacing. When multiple pulse sequence segments are run simultaneously ondifferent shells, various embodiments of the present disclosurecompensate for interactions between the shells that result from the B-Sshift. In one example, a first pulse sequence segment with a firstfrequency ω_(RF1) is applied to the substance and a second pulsesequence segment with a second frequency ω_(RF2) is applied to thesubstance. An offset Δω_(RF) between the first frequency and the secondfrequency induces an extra phase shift on the transverse magnetization.This so-called “Bloch-Siegert” shift is designated herein as φ_(BS). Incases where Δω_(RF) is much larger (e.g., larger than 2ω₁) than thefrequency ω₁, the phase shift for on-resonance magnetization can bedetermined by:

$\begin{matrix}{\phi_{BS} = {( \frac{\theta}{2} ){\frac{\omega_{1}}{\Delta \; \omega_{RF}}.}}} & {{Eq}.\mspace{14mu} 7}\end{matrix}$

where θ is the nominal tipping angle of the pulse. The nominal tippingangle can be determined by:

θ=γ2πt _(p)  Eq. 8

where t_(P) is the duration of the pulse and γ is the gyromagnetic ratioof the nucleus of interest.

The NMR pulse sequence shown in FIG. 19 includes a plurality ofinterposed pulse sequence segments (N_(S)). Various embodiments of thepresent disclosure compensate for the B-S phase shift by modulating thephase and/or timing of excitation pulses within the plurality ofinterposed pulse sequence segments. The phase shift for a spin in ashell consists of the standard Larmor phase shift between two refocusingpulses. This phase shift can be determined by adding the result ofEquation 6 to the phase shifts induced by the pulse sequence segments(e.g., N_(S)−1) applied to previous shells. For the pulse sequencesegment applied to the first shell, the phase shift between theexcitation pulse and the first refocusing pulse remains half the totalphase shift because the B-S phase shift is proportional to pulseduration. In one example, the B-S phase shift is proportional to thepulse duration when the refocusing pulses are twice as long and have thesame amplitude as the excitation pulse (e.g., the excitation pules is 90degrees and the excitation pulses are 180 degrees).

For a second pulse sequence segment applied to a second shell, thisproportionally is not fulfilled. During the time interval between whenthe excitation pulse of the second pulse sequence segment and the firstrefocusing pulse of the second pulse sequence segment are applied, arefocusing pulse is applied to the first shell as part of the firstpulse sequence segment. This refocusing pulse adversely affects thesecond pulse sequence segment. If the refocusing pulse is a 180 degreepulse, then the associated B-S phase shift is twice as long, as comparedwith the 90 degree excitation pulse. The total phase shift caused byfirst pulse sequence segment and the first shell can be determined by:

$\begin{matrix}{{\Delta \; \phi_{{BS},2}} = {{- ( \frac{\pi}{4} )}\frac{\omega_{1}}{\Delta \; \omega_{RF}}}} & {{Eq}.\mspace{14mu} 9}\end{matrix}$

The first pulse sequence segment and second pulse sequence segment alsoproduce phase shifts that affect any potential third pulse sequencesegment. Furthermore, each subsequent pulse sequence segment is affectedby phase shifts produced by segments applied before the subsequentsegment. These phase shifts can be compensated by determining andsumming the phase shift contribution of each previous pulse sequencesegment. Equation 10 below can be used to determine the total phaseshift for a plurality of previous pulse sequence segments:

$\begin{matrix}{{\Delta \; \phi_{{BS},k}} = {{- \frac{\pi}{4}}\frac{\omega_{1}}{\Delta \; \omega_{RF}}( {1 + \frac{1}{2} + \frac{1}{3} + {\ldots \mspace{14mu} \frac{1}{k - 1}}} )}} & {{Eq}.\mspace{14mu} 10}\end{matrix}$

The integer k is the pulse sequence segment of interest and (k−1) is thenumber of pulse sequence segments that contribute to the total phaseshift. Using Equation 10, the B-S phase shift can be corrected byreplacing the standard excitation pulse (e.g., 90_(x)) within the k-thpulse sequence segment with an excitation pulse that has a modulatedphase. In a particular embodiment, the phase of the excitation pulse ismodulated by the total phase shift produced by the previous pulsesequence segments. In other words, the phase of the excitation pulsewithin the k-th pulse sequence segment is equal to the phase of theexcitation pulse in the first segment minus the result of Equation 10(e.g., 90−Δφ_(BS,k)).

Illustrative embodiments of the present disclosure are also directed tocorrecting for the B-S phase shift when the phase shift is not constantwithin a single shell. Equation 9 shows that the B-S phase shift canvary within a shell because the offset frequency (Δω_(RF)) varieslinearly across the shell. This phenomenon can be addressed by shiftingthe position of the excitation pulse for the k-th pulse sequence segmentby:

$\begin{matrix}{{\delta\tau}_{k} = {\frac{t_{\pi}}{2}{( {1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + {\ldots \mspace{14mu} \frac{1}{( {k - 1} )^{2}}}} ).}}} & {{Eq}.\mspace{14mu} 11}\end{matrix}$

In Equation 11, t_(π) is the length of the excitation pulse within thefirst pulse sequence segment. In this manner, the B-S phase shift can becorrected by replacing a standard time interval (T_(P)) between theexcitation pulses within the first and second segments with a timeinterval (T_(P)) that is varied. In a particular embodiment, the initialtime interval (T_(P)) is modulated by the result of Equation 11 (e.g.,δ_(Tk)). In other words, the time interval between the excitation pulsein the k-th pulse sequence segment and the excitation pulse of the nextpulse sequence segment is equal to the initial time interval (T_(P))plus the result of Equation 11 (e.g., δ_(Tk)). In this manner, variousembodiments of the present disclosure account for the B-S phase shiftwithin interposed pulse sequence segments.

In various embodiments, the multi-segment sequences described herein areapplied at a plurality of different frequencies. In some embodiments,the segments within each sequence are interposed. To apply the sequencesand detect resonant signals, various embodiments of the presentdisclosure are directed to NMR electronics that are configured to switchbetween a transmitting mode and a receiving mode. Within a transmittingmode, the electronics are further configured to switch between variousfrequencies so that the coil can apply pulse sequence segments atdifferent frequencies. Within a receiving mode, the electronics areconfigured to switch between various frequencies so that the coil andelectronics can detect resonant signals at different frequencies. Invarious embodiments, the switching of frequencies is performed accordingto a particular schedule.

FIG. 14 shows a switching schedule 1412 for the NMR pulse sequence 1400in accordance with one embodiment of the present disclosure. In thespecific example, the switching schedule 1412 begins with a first set oftime intervals 1414. During the first set of time intervals 1414, thebroadband NMR electronics are set to a transmitting mode. The first setof time intervals includes four time intervals 1416, 1418, 1420, 1422.During the first time interval 1416, the electronics are set to a firstfrequency (ω_(RF1)) so that the coil can apply the first excitationpulse 1406 of the first pulse sequence segment 1402. During the secondtime interval 1418, the electronics are set to a second frequency(ω_(RF2)) so that the coil can apply the first excitation pulse 1406 ofa second pulse sequence segment 1404. During the third time interval1418, the electronics are set to the first frequency (ω_(RF1)) so thatthe coil can apply the first refocusing pulse 1408 of the first pulsesequence segment 1402. During the fourth time interval 1422, theelectronics are set to the second frequency (ω_(RF2)) so that the coilcan apply the first refocusing pulse 1408 of the second pulse sequencesegment 1404. As explained above, the frequency (e.g., ω_(RF1)) within apulse segment or a single pulse may not be a single frequency. Thefrequency within a pulse sequence segment or a single pulse can varyover a set of frequencies (e.g., over a range of frequencies).

Following the first set of time intervals 1414, a second set of timeintervals 1424 begins. During the second set of time intervals 1424, thebroadband NMR electronics switch to a receiving mode of operation. Thesecond set 1424 includes two time intervals 1426, 1428. The first timeinterval 1426 is dedicated to detecting a resonant signal at the firstfrequency (ω_(RF1)) generated by the first pulse sequence segment 1402(e.g., within the first shell). In the embodiment shown in FIG. 14, asingle echo 1410 is detected at the first frequency. The second timeinterval 1428 is dedicated to detecting a resonant signal at the secondfrequency (ω_(RF2)) generated by the second pulse sequence segment 1404(e.g., within the second shell). Again, a single echo 1410 is detectedat the second frequency.

Next, a third set of time intervals 1430 follows. During the third setof time intervals 1430, the broadband NMR electronics are switched backto a transmitting mode of operation. During this set of time intervals1430, one more refocusing pulse 1408 is applied at each of the twodifferent frequencies (e.g., ω_(RF1) and ω_(RF2)). Then, a fourth set oftime intervals 1432 follows. During the fourth set of time intervals1432, the broadband NMR electronics are switched to a receiving mode ofoperation. During the fourth set of time intervals 1432, resonantsignals (e.g., echoes) 1410 are detected at each of the two differentfrequencies (e.g., ω_(RF1) and ω_(RF2)). The third and fourth sets oftime intervals 1430, 1432 can be repeated a plurality of times (e.g.,N_(E)=10, N_(E)=100, and N_(E)=1000) until the NMR pulse sequence comesto an end. In some embodiments, the time intervals have equal lengthsacross the switching schedule. In other embodiments, the time intervalshave varying lengths. In various embodiments, the time intervals are atleast as long as the excitation pulse and/or refocusing pulse that theyare dedicated to applying. Also, the time intervals are at least as longas the echoes that they are dedicated to detecting. In furtherembodiments, the length of the time intervals is no greater than 1 ms.In yet further embodiments, the length of the time intervals is nogreater than 100 μs.

FIGS. 14 and 16 show two switching schedules 1408, 1608 for NMR pulsesequences, 1400, 1600 in accordance with embodiments of the presentdisclosure. In FIG. 14, the switching schedule 1408 also modulatesbetween a transmitting mode 1410 and a receiving mode 1412. In thiscase, within each mode, the broadband NMR electronics are switchedbetween three different frequencies (e.g., ω_(RF1), ω_(RF2) andω_(RF3)). Similarly, in FIG. 16, the switching schedule 1608 alsomodulates between a transmitting mode 1610 and a receiving mode 1612 andwithin each mode, the broadband NMR electronics are switched betweenN_(S) number of different frequencies (e.g., ω_(RF1), ω_(RF2), ω_(RF3),. . . , ω_(RFNs)). In this manner, various embodiments of the presentdisclosure apply pulse sequence segments at various differentfrequencies and detect resonant signals from a plurality of differentshells within the substance.

FIG. 17 shows a plot 1700 of measured signal amplitude versus time inaccordance with one embodiment of the present disclosure. Morespecifically, FIG. 17 shows asymptotic echoes that were detected for anNMR sequence with two interposed pulse sequence segments (e.g.,N_(S)=2). The segments generated resonant signals within two shells of adoped-water sample. The doped-water sample had a T₂ relaxation time of120 ms. The two interposed pulse sequence segments were applied to thesample using broadband NMR electronics. The first pulse sequence segmentwas applied at 2.0 MHz (e.g., ω_(RF)/2π=2.0 MHz) and the frequencydifference between the first pulse sequence segment and the second pulsesequence segment was 20 kHz (e.g., Δω_(RF)/2π=20 kHz=11.8 ω₁). Also, theexcitation pulses for each segment had a duration of 140 μs (e.g.,T₉₀=140 μs). The echoes between each shell were separated by 500 μs(e.g., T_(S)=500 μs) and the sequence was repeated 128 times (e.g.,N=128). The receiver frequency was kept constant at the center frequencyof the first pulse sequence segment (e.g., ω_(RF)/2π=2.0 MHz) so thefirst echo sequence was demodulated to zero frequency (e.g., baseband).The second echo sequence was demodulated to an offset frequency of 20kHz (e.g., Δω_(RF)/2π=20 kHz). The echoes from each resonant signal weredistinguished by the placement in time (e.g., T_(S)=500 μs). In variousother embodiments, the echoes can also be distinguished by theirfrequency content.

Illustrative embodiments of the present disclosure are also directed tomulti-segment sequences that are applied to generate interactionsbetween shells and these interactions between shells are used todetermine an NMR property. Such multi-segment sequences influencemagnetization in one shell of a substance by manipulating spins in othershells of the substance. In one embodiment, such a method includesapplying an NMR pulse sequence to the substance. The NMR pulse sequenceincludes at least a first pulse sequence segment at a first set offrequencies and a second pulse sequence segment at a second set offrequencies. The second pulse sequence segment generates a resonantsignal within a shell of the substance and the first pulse sequencesegment generates a characteristic within the resonant signal throughinteraction with another shell. The resonant signal is detected and anNMR property is determined based upon the characteristic within thedetected resonant signal.

In various embodiments, the characteristic may be an imaginary componentwithin the detected resonant signal that is introduced by the firstpulse sequence segment. For example, the first pulse sequence segmentmay introduce an asymmetry in longitudinal magnetization within theshell. In another example, the characteristic may be a phase shiftwithin the detected resonant signal.

In some embodiments, the NMR property that is determined is an NMRproperty of the substance, such as a long spin-lattice T₁ relaxationtime of the substance. In another example, the NMR property is aproperty of the NMR measurement itself. In one specific example, theproperty of the NMR measurement is the magnitude of the appliedoscillating field. Details of how interactions between shells can beused to determine (1) a long spin-lattice T₁ relaxation time of thesubstance and (2) a magnitude of the applied oscillating field aredescribed below.

As explained above, multi-segment sequences can be advantageously usedto generate interaction between a plurality of shells, to detect spinswith long spin-lattice relaxation times (T₁), and to determine thelength of such relaxation times. Measurements produced from suchsequences can be used as log quality control indicators. For example,the measurements can be used to warn an operator about incompletepolarization during fast logging operations. Such multi-segmentsequences can function as “partial” saturation recovery sequences.

FIG. 18 shows a multi-segment sequence 1800 for determining T₁relaxation time in accordance with one embodiment of the presentdisclosure. The sequence 1800 includes a first pulse sequence segment1802 at a first set of frequencies (ω_(RF1)) that is applied to a firstshell and a second pulse sequence segment 1804 at a second set offrequencies (ω_(RF2)) that is applied to a second shell. The pulsesequence 1800 includes a waiting period (T_(W)) between the first pulsesequence segment 1802 and the second pulse sequence segment 1804. Insome cases, the waiting period (T_(W)) is between 1 ms and 10 s. In onespecific example, the waiting period (T_(W)) is less than 1 s. Also, inanother specific example, the pulse sequence segments are CPMGsequences. In some cases, the second pulse sequence segment 1804 isinitiated before the first shell reaches thermal equilibrium. If thewaiting period (T_(W)) is much greater than the T₁ relaxation time, thenthe first pulse sequence segment 1802 will not have the desiredinteraction on the second shell. When the waiting period (T_(W)) isapproximately equal to or smaller than the T₁ relaxation time, then thefirst pulse sequence segment 1802 will have the desired interaction onthe second shell and this interaction can be detected to determinewhether the waiting period (T_(W)) is bigger or smaller than the T₁relaxation time.

An average frequency (ω_(RF2)) of the second pulse sequence segment 1804is offset from an average frequency (ω_(RF1)) of the first pulsesequence segment 1802 by a frequency difference (Δω_(RF)). In variousembodiments, the frequency difference is less than 10ω₁. In somespecific embodiments, the frequency difference is between 1ω₁ and 4ω₁.The amount of interaction between the first shell and the second shellcan be controlled by varying the frequency difference (Δω_(RF)) and/orthe waiting period (T_(W)). The first pulse sequence segment 1802generates an asymmetry in at least a portion of the longitudinalmagnetization with respect to a static frequency offset axis of thesecond pulse sequence segment 1804. The asymmetry introduces a non-zeroimaginary component into echoes generated within the second shell. Thisimaginary component decays exponentially as exp(−T_(W)/T₁). Thisimaginary component of the resonant signal within the second shell isdetected. The imaginary component and the known value of the waitingperiod (T_(W)) can be used to determine the T₁ relaxation time. In somecases, the partial saturation recovery sequences advantageously increaseSNR for nuclei with long T₁ components. In contrast, in conventionalsaturation recovery sequences, SNR approaches zero as T₁ approachesinfinity.

FIG. 19 shows a simulated plot 1900 of asymptotic echo amplitude versusecho acquisition time in accordance with one embodiment of the presentdisclosure, while FIG. 20 shows a measured plot 2000 of asymptotic echoamplitude versus echo acquisition time in accordance with one embodimentof the present disclosure. In particular, the Figures show simulated andmeasured asymptotic echo amplitudes for a partial saturation recoverysequence. In this case, the sequence includes a waiting period of 10 msbetween segments (e.g., T_(W)=10 ms). Each pulse sequence segment was aCPMG sequence. The partial saturation recovery sequence was applied to adoped-water sample. The doped-water sample had a T₁ and T₂ relaxationtime of approximately 120 ms (e.g., T₁≈T₂=120 ms). The pulse sequencewas applied to the sample using a broadband NMR system. The Larmorfrequency of the first shell was 0.94 MHz and the frequency differencebetween the shells was 10 kHz (e.g., Δω_(RF)/2π=10 kHz). The excitationpulses for each segment were 70 μs in length (e.g., T₉₀=70 μs). The echospacing within each shell was 4 ms (e.g., T_(E)=4 ms) and the pulsesequence was repeated 128 times (e.g., N=128). As shown in FIGS. 19 and20, the measured asymptotic echo amplitude corresponds well with thesimulated asymptotic echo amplitude for the partial saturation recoverysequence. The asymptotic echo produced by the second shell has anon-zero imaginary component 1902. As explained above, the non-zeroimaginary component can be used to determine the T₁ relaxation time.Further measurements demonstrated similar favorable results for variousdifferent values of the waiting period (T_(W)).

As explained above, in another illustrative example, a multi-segmentsequence is used to determine the magnitude of an applied oscillatingfield (B₁). Various embodiments of the present disclosure are directedto a fast and accurate method that determines an average magnitude of anRF magnetic field (B₁), or equivalently a nutation frequency (ω₁=γB₁),that is applied by an NMR system. The multi-segment sequence uses theBloch-Siegert phase shift (B-S phase shift) to determine the magnitudeof an applied oscillating field.

FIG. 21 shows a multi-segment sequence 2100 for determining an appliedoscillating field (B₁). The sequence 2100 includes a first pulsesequence segment 2102 at a first frequency (ω_(RF1)) (e.g., set offrequencies) and a second off resonant pulse sequence segment 2104 at asecond frequency (ω_(RF2)) (e.g., set of frequencies). The differencebetween the two pulses is Δω_(RF1). In the pulse sequence segment ofFIG. 21, the first segment 2102 includes an excitation pulse 2106, arefocusing pulse 2108 and an echo 2110. In various embodiments, theexcitation pulses have a length of T₉₀ and the refocusing pulses have alength of T₁₈₀. In this case, the first segment 2102 is a Hahn spin-echosequence (SE). The second segment 2104 includes an off-resonant pulse2112 that is applied after the excitation pulse 2106. The second segment2104 also includes another off-resonant pulse 2114 that is applied afterthe refocusing pulse 2108. The off-resonant pulses each have a length ofT_(BS).

FIG. 22 shows another multi-segment sequence 2200 for measuring anapplied oscillating field (B₁). In this embodiment, the sequence 2200includes a first pulse sequence segment 2202 at a first frequency(ω_(RF1)) and a second off-resonant pulse sequence segment 2204 at asecond frequency (ω_(RF2)). The first segment 2202 includes anexcitation pulse 2206 and refocusing pulse 2208, and an echo 2210. Therefocusing pulse 2208 and the echo 2210 (e.g., refocusing cycle) arerepeated a number of times (N_(E)). In this case, the first segment is aCPMG sequence. The second segment 2204 includes a first off-resonantpulse 2212 that is applied after the excitation pulse 2206 and anothersecond off-resonant pulse 2214 that is applied after the refocusingpulse 2208. As shown in FIG. 22, the pulse sequence segments 2202, 2204are interposed within each other. In this case, the second off-resonantpulse 2212 is repeated after each refocusing pulse 2208 (e.g., N_(E)number of times). Also, in this case, the first off-resonant pulse 2212has a length of T_(BS), while the second off-resonant pulse 2214 has alength of 2T_(BS).

FIG. 23 shows another multi-segment sequence 2300 for measuring anapplied oscillating field (B₁). In this case, a second off resonantpulse sequence segment 2304 includes a second off-resonant pulse 2314that is applied after an echo 2310. The multi-segment sequences shown inFIGS. 21-23 are specific examples and the embodiments presented hereinare not limited to any specific sequences and pulse lengths.

In these specific examples, the pulses have a length of T_(BS) and2T_(BS) and the pulses introduce B-S phase shifts that are φ_(BS) and2φ_(BS), respectively (e.g., because φ_(BS)=ω₁ ²T_(BS))(2Δω_(RF))). SuchB-S phase shifts can also be produced by varying other pulsecharacteristics. In particular, such phase shifts can be produced bychanging the pulse length (T_(BS)), the pulse amplitude (ω₁), or thefrequency offset (Δω_(RF)).

In illustrative embodiments, the multi-segment sequences (e.g., 2100,2200, 2300, are applied a plurality of times (e.g., a number of“scans”). In some embodiments, the pulses have equal and oppositefrequency offsets (±Δω_(RF)), which removes the dependence of B-S phaseshift (φ_(BS)) on resonant frequency offset, as shown in Equation 24below. For example, in a first application of a multi-segment sequence(e.g., a first scan), the frequency offset is +Δω_(RF), while in asecond application of the multi-segment sequence (e.g., second scan) thefrequency offset is −Δω_(RF).

The first and second off-resonant pulses induce a B-S phase shift(φ_(BS)) in the echoes of the resonant signal and this B-S phase shiftcan be used to determine the applied oscillating field (B₁). Asexplained above, the pulse sequences are applied using an NMR system. Insome embodiments, the NMR system is a broadband system that appliesoff-resonant pulses with a frequency offset (Δω_(RF)) of several ω₁ fromthe Larmor frequency. For example, at a Larmor frequency of 2 MHz and anutation frequency ω₁=2π×10 kHz (corresponding to T₉₀=25 μs), the offsetfrequency might be 8ω₁=2π×80 kHz. The NMR system also includes a coil toexcite nuclear spins and produce a resonant signal within a shell. Thecoil produces a time-varying linear RF magnetic field that can beexpressed as the sum of two circularly-polarized magnetic fields usingthe following equation:

$\begin{matrix}{{{\cos ( {\omega_{0}t} )} = \frac{{\exp ( {\; \omega_{0}t} )} + {\exp ( {{- {\omega}_{0}}t} )}}{2}},} & {{Eq}.\mspace{14mu} 12}\end{matrix}$

where ω₀ is the excitation frequency, t is time, and i=√{square rootover (−1)}. The two fields rotate clockwise and counter-clockwise withtime. The effect of the counter-clockwise rotating field on the resonantsignal is to shift the resonant frequency by an amount (ω_(BS)), asshown by the following equation:

$\begin{matrix}{\omega_{BS} = {\frac{( {\gamma \; B_{1}} )^{2}}{4\omega_{0}} \equiv \frac{\omega_{1}^{2}}{4\omega_{0}}}} & {{Eq}.\mspace{14mu} 13}\end{matrix}$

where B₁ is the amplitude of each circularly-polarized RF field. Thecounter-clockwise rotating field can be viewed as being offset infrequency from the resonant (clockwise rotating) field by an amountω₀−(−ω₀)=2ω₀. In most cases, ω₁ is much less than ω₀ and this so-calledB-S frequency shift is small and can be ignored. However, it is possibleto increase the shift by decreasing the frequency offset from 2ω₀ tosome other value Δω_(RF). As explained above, off-resonant RF pulses ata frequency (ω₀−Δω_(RF)) can be applied for increasing the shift. Theeffect of such an off-resonant excitation pulse is expressed by thefollowing equation:

$\begin{matrix}{\omega_{BS} = \frac{\omega_{1}^{2}}{2\Delta \; \omega_{RF}}} & {{Eq}.\mspace{14mu} 14}\end{matrix}$

where Δω_(RF) is the frequency offset of the off-resonant pulse, and ω₁is γB₁ (e.g., ω₁≡γB₁). In illustrative embodiments, the frequency offset(Δω_(RF)) is much larger than ω₁ and the off-resonant pulse does notexcite any additional magnetization and thus does not change theamplitude of the spin echo. However, the off-resonant pulse does producea measurable phase shift. This phase shift effect can be described byusing the rotating frame of the pulse. In the rotating frame, theeffective magnetic field for the spin packet at Δω_(RF) is given by:

γB _(eff)=√{square root over ((Δω_(RF))²+ω₁ ²)}  Eq. 15

The off-resonant pulse modifies the magnitude of the effective field,and thus the precession frequency, from its free-precession value ofΔω_(RF) by an amount that is the B-S phase shift.

FIG. 24 shows an effective on-resonance magnetic field in the rotatingframe of the off-resonant pulse. Using trigonometry, as shown in FIG.24, the following relationship is determined:

$\begin{matrix}{\omega_{eff}^{2} = {( {{\Delta \; \omega_{RF}} + \omega_{BS}} )^{2} =  {( {\Delta \; \omega_{RF}} )^{2} + \omega_{1}^{2}}\Rightarrow{\omega_{BS} \approx \frac{\omega_{1}^{2}}{2\Delta \; \omega_{RF}}} }} & {{Eq}.\mspace{14mu} 16}\end{matrix}$

Since the effective field is approximately aligned to the static field(z-axis) far off-resonance (e.g., when Δω_(RF) much greater than ω₁),the pulse will produce almost no additional magnetization. However, itwill produce additional precession about the z-axis, resulting in aphase shift for the resonant signal at Δω_(RF) of:

$\begin{matrix}{\varphi_{BS} = {{\int_{0}^{T_{BS}}{{\omega_{BS}(t)}\ {t}}} = {\int_{0}^{T_{BS}}{\frac{( {\gamma \; {B_{1}(t)}} )^{2}}{2\Delta \; {\omega_{RF}(t)}}\ {t}}}}} & {{Eq}.\mspace{14mu} 17}\end{matrix}$

where T_(BS) is the duration of the off-resonant pulse. Because themagnitude of the effect decreases only as the inverse of the offsetfrequency (Δω_(RF)), even frequency-selective pulses applied faroff-resonance can produce significant B-S phase shifts. The precisevalue of the B-S phase shift depends on the amplitude and frequencyprofile of the off-resonant pulse, as shown in Equation 17. In the caseof fixed-amplitude (rectangular) and fixed-frequency pulses, Equation 17simplifies to:

$\begin{matrix}{\varphi_{BS} = {{T_{BS}( \frac{\omega_{1}^{2}}{2{\Delta\omega}_{RF}} )} = {\theta_{nom}( \frac{\omega_{1}}{2\Delta \; \omega_{RF}} )}}} & {{Eq}.\mspace{14mu} 18}\end{matrix}$

where θ_(nom) is the nominal tipping angle of the off-resonant pulse(e.g., θ_(nom)≡ω₁T_(BS)). In an inhomogeneous static field the B-S phaseshift is also a function of the resonant frequency offset (Δω₀) within ashell, as shown below:

$\begin{matrix}{{\varphi_{BS}( {\Delta \; \omega_{0}} )} = \frac{\omega_{1}^{2}T_{BS}}{2( {{\Delta \; \omega_{RF}} - {\Delta \; \omega_{0}}} )}} & {{Eq}.\mspace{14mu} 19}\end{matrix}$

Rectangular pulses in a constant static field gradient excite afrequency span of approximately 2ω₁, (e.g., the region where |Δω₀|≦ω₁),thus defining the shell. In some embodiments, where Δω_(RF) is muchlarger than ω₁, Δω_(RF) is also much larger than |Δω₀| within theexcited volume (e.g., shell). The denominator in Equation 19 can then beexpanded as a Taylor series to determine the following relationship:

$\begin{matrix}{{\varphi_{BS}( {\Delta \; \omega_{0}} )} = {{T_{BS}( \frac{\omega_{1}^{2}}{2{\Delta\omega}_{RF}} )}\lbrack {1 + \frac{{\Delta\omega}_{0}}{\Delta \; \omega_{RF}} + {O( {\Delta \; \omega_{0}^{2}} )}} \rbrack}} & {{Eq}.\mspace{14mu} 20}\end{matrix}$

The first-order dependence on resonant frequency can be removed bytaking the difference between two applications (e.g., scans) ofmulti-segment sequences (e.g., 2200, 2300) with offset frequencies of+Δω_(RF) and −Δω_(RF), as explained above. In this case, the phase shiftis approximately constant across the excited sample volume, and there isalmost no distortion of the echo shape. The shift is given by:

$\begin{matrix}\begin{matrix}{{{\varphi_{BS}( {{+ \Delta}\; \omega_{0}} )} - {\varphi_{BS}( {{- \Delta}\; \omega_{0}} )}} = {{T_{BS}( \frac{\omega_{1}^{2}}{{\Delta\omega}_{RF}} )}\lbrack {1 + {O( {\Delta\omega}_{0}^{2} )}} \rbrack}} \\{\approx {T_{BS}( \frac{\omega_{1}^{2}}{\Delta \; \omega_{RF}} )}}\end{matrix} & {{Eq}.\mspace{14mu} 21}\end{matrix}$

Equation 21 can be re-written to solve for the applied oscillating field(B₁) based upon the measured B-S phase shift (φ_(BS)), the length of theoff-resonant pulse (T_(BS)), the frequency offset (Δω_(RF)), and theexcitation frequency (ω₀), as shown below:

$\begin{matrix}{B_{1} \approx {\frac{1}{\gamma}\sqrt{\frac{{\Delta\omega}_{RF}}{T_{BS}}\lbrack {{\varphi_{BS}( {+ {\Delta\omega}_{0}} )} - {\varphi_{BS}( {{- \Delta}\; \omega_{0}} )}} \rbrack}}} & {{Eq}.\mspace{14mu} 22}\end{matrix}$

The B-S phase shift (φ_(BS)) can be determined more accurately byincreasing the resonant signal. The resonant signal can be increased bygenerating multiple spin echoes and then adding the echoes. A CPMGsequence, such as the one shown in FIG. 22 or 23, can be used for thispurpose. In various embodiments, in order to measure the B-S shift witha CPMG sequence, the CPMG condition is satisfied (e.g., the initialtransverse magnetization is aligned with the effective axis of therefocusing cycle) and the initial transverse magnetization isphase-shifted by the first off-resonant pulse. As a result, theeffective refocusing axis is also rotated by the same amount. A secondoff-resonant pulse that creates a phase shift of 2φ_(BS) can be added tothe refocusing cycle for this purpose. This behavior can be obtained byincreasing the length of the second off-resonant pulse by a factor of 2,by increasing the amplitude of the off-resonant pulse by a factor of √2,or by a combination of both such techniques. In some embodiments, theamplitudes of the off-resonant pulses are constant, thus allowing thesequence to be transmitted using highly-efficient nonlinear poweramplifiers. In various embodiments, the second off-resonant pulseswithin each CPMG refocusing cycle can be applied before the echo (e.g.,2200), or after the echo (e.g., 2300). The spin dynamics of thesesequences are similar, except for a reversal in the sign of the phaseshift (φ_(BS)). The application of RF pulses is followed by a certain“dead time” where the receiver is not used (e.g., because of pulse feedthrough, duplexer switching time or other reasons). The gap between theapplication of RF pulses and the generation of echoes is larger in themulti-segment sequence shown in FIG. 23 than the multi-segment sequenceshown in FIG. 22 and so the sequence in FIG. 22 is less susceptible todead time effects. As a result, shorter echo spacing is possible, whichresults in higher SNR and more accurate estimation of the B-S phaseshift (φ_(BS)).

In illustrative embodiments, the second segment and its off-resonantpulses are phase cycled. In some cases, the off-resonant pulses excitesmall but often non-negligible amounts of transverse magnetization,which produce amplitude variations in the final echo and can make itdifficult to measure the phase shift (φ_(BS)) precisely. This effect canbe particularly pronounced for rectangular pulses, which may have poorfrequency selectivity. Such unwanted magnetization can be eliminated byphase cycling the off-resonant pulses. Table 1 shows an example offour-part phase cycles that can be used to measure the B-S phase shiftfor a given frequency offset (Δω_(RF)). The phase shifts in Table 1 areshown in multiples of π/2. The four-part phase cycles include twophase-alternating pairs (PAPs) with opposite phases for the off-resonantpulses. The cycle is repeated for a frequency offset of −Δω_(RF) and thephases are subtracted from each other to get the final value of thephase shift (φ_(BS)), as shown in Equation 22. This differentialcomputation also makes the result independent of the absolute phase ofthe echo. Thus, in some cases, a total of four PAPs are sufficient formeasuring the B-S phase shift.

TABLE 1 Step 0 1 2 3 Excitation 2 2 0 0 Pulses Refocusing 3 3 1 1 PulsesOff-resonant 2 0 2 0 Pulses Acquisition 2 2 0 0

In illustrative embodiments, the length of the refocusing pulses(T_(BS)) is an integer multiple of 2π/Δω_(RF). In such embodiments, therotating frames of the first sequence segment (e.g., CPMG pulses) andthe second sequence segment (e.g., off-resonant pulses) are alignedafter each off-resonant pulse. In some cases, it may not be possible toensure that this synchronicity condition is precisely satisfied (e.g.,because of pulse transients, limited timing precision of thespectrometer, or other factors). For example, pulse turn-on and turn-offtransients may reduce the effective length of both the firstoff-resonant pulse (e.g., T_(BS)) and the second off-resonant pulse(e.g., 2T_(BS)) by the same amount (Δt). As a result, the effect can beremoved by lengthening both pulses by Δt. In the absence of thiscorrection, there will be a static phase offset between the rotatingframes of the off-resonant pulses and the CPMG pulses. As a result, theecho will exhibit the same phase offset, which is given by:

φ_(off)=2Δω_(RF) ×Δt  Eq. 23

where the factor of two is used because of two applications ofmulti-segment sequences with opposite values of Δω_(RF) (e.g., a firstscan at +Δω_(RF) and a second scan at −Δω_(RF)). Such static phaseoffsets can be removed by applying the multi-segment sequence with twovalues of T_(BS): (T_(BS,1)) and (T_(BS,2)). In such an embodiment,measured phase shifts (including the offset) may be given by φ₁ and φ₂.The true phase shifts φ_(BS,1)=φ₁−φ_(off) and φ_(BS,2)=φ₂−φ_(off), canbe estimated because the shifts linearly depend on T_(BS):

$\begin{matrix}{\frac{\varphi_{1} - \varphi_{off}}{\varphi_{2} - \varphi_{off}} = { \frac{T_{{BS},1}}{T_{{BS},2}}\Rightarrow\varphi_{off}  = \frac{{\varphi_{1}T_{{BS},1}} - {\varphi_{2}T_{{BS},1}}}{T_{{BS},2} - T_{{BS},1}}}} & {{Eq}.\mspace{14mu} 24}\end{matrix}$

The phase of a complex echo signal z(t)=x(t)+iy(t) can be estimated byfinding the average in-phase and quadrature components, as follows:

$\begin{matrix}{\varphi = {{\tan^{- 1}( \frac{\int_{0}^{T_{acq}}{{x(t)}\ {t}}}{\int_{0}^{T_{acq}}{{y(t)}\ {t}}} )} \approx {\tan^{- 1}( \frac{\sum\limits_{i = 0}^{N_{acq} - 1}{x\lbrack i\rbrack}}{\sum\limits_{i = 0}^{N_{acq} - 1}{y\lbrack i\rbrack}} )}}} & {{Eq}.\mspace{14mu} 25}\end{matrix}$

where N_(acq) data points are measured within an acquisition window oflength T_(acq). The error in this estimate is minimized when the windowhas approximately the same width as the echo itself. The next process isto estimate ω₁ by inverting the measured B-S phase shift. According toEquation 24, two measurements are sufficient since the phase shift(φ_(BS)) is dependent on ω₁ and known properties of the off-resonantpulses (e.g., length and frequency offset).

In illustrative embodiments, variations in pulse parameters within thefirst pulse sequence segment, such as flip angles of the excitation andrefocusing pulses, do not complicate the inversion process by causingchanges in the B-S phase shift (φ_(3s)). The flip angle of a pulselength (T) can be determined based upon the pulse length (T), thegyromagnetic ratio (γ), and the magnitude of the applied oscillatingfield (B₁) (e.g., flip angle is equal to γB₁T). FIG. 25 shows phase ofasymptotic echoes as a function of various pulse lengths foroff-resonant pulses (T_(BS)). In particular, FIG. 25 shows that the B-Sphase shift (φ_(BS)) is substantially constant for a wide range of flipangles. As a result, ω₁ can be estimated accurately using one or twophase-shift measurements. FIG. 26 shows amplitude of asymptotic echoesas a function of various pulse lengths for off-resonant pulses (T_(BS)).In particular, FIG. 26 shows that the echo amplitude is substantiallyunaffected by the off-resonant pulses. The plots in FIG. 25 and FIG. 26were generated by normalizing the nutation frequency (e.g., settingω₁=1), setting the ratio of lengths of the refocusing and excitationpulses within the first sequence segment to 2, and the frequency offset(Δω_(RF)) was set to 8ω₁. As a result, the nominal B-S phase shiftsexpected for T_(BS)=2π and T_(BS)=π were π/4)(45° and π/8)(22.5°,respectively. The sequence for measuring the B-S shift was implementedon a broadband NMR system, as described herein. The pulse lengths anddelays were set to integer multiples of the frequency offset (Δω_(RF))to minimize static phase offsets. In addition, a small timing correction(on the order of 1 μs) was applied between the excitation pulse and thefirst refocusing cycle. This correction ensured that the initialtransverse magnetization was aligned with the effective refocusing axis.

FIG. 27 shows a measured B-S phase shift for a doped-water sample forvarious off-resonant pulse lengths (T_(BS)). The plot in FIG. 27 wasgenerated by applying a multi-segment sequence 2300, as shown in FIG.23, to a doped-water sample. The doped water had a T₂ of approximately110 ms. The parameters of the multi-segment sequence included:ω_(RF)/2π=1.48 MHz; T_(E)=2.4 ms; N_(E)=50; Δω_(RF)/2π=25 kHz;excitation pulse length=80 μs; and refocusing pulse length=160 μs.Static phase offset was estimated and removed by using the smallest andlargest values of T_(BS), as shown in Equation 24. The remaining phaseshift is a linear function of T_(BS) with a slope corresponding toT₉₀=102 μs, (e.g., ω₁/2π=1/(4T₉₀)=2.45 kHz). In this case, two values ofT_(BS) were used to measure T₉₀.

The results in FIG. 27 were in agreement with conventional approachesfor determining the applied oscillating field, such as using measurednutation curves. A measured nutation curve was determined by varying theexcitation and refocusing pulse widths within the first segment, whilekeeping the ratio between them fixed. The resultant echo amplitudes wereplotted and the location of the peak was found. Such a measured nutationcurve is shown in FIG. 28. As shown in FIGS. 27 and 28, the twotechniques described above (e.g., based on measuring the B-S phase shiftand a nutation curve, respectively) are in good agreement, except forthe fact that the peak of the nutation curve occurs at slightly shorterpulse lengths (e.g., 96 is as opposed to 102 μs). The difference iscaused by a spin-dynamics effect, namely, the multiplicity of coherencepathways that contribute to the asymptotic CPMG echo shape ininhomogeneous fields. Similar results were obtained at other offset andLarmor frequencies, showing that the using the B-S phase shift can be afaster and more accurate way to measure the magnitude of the B₁ fieldand calibrate pulse lengths, as compared to conventional methods.

Illustrative embodiments are also directed to determining the magnitudeof an applied oscillating field (B₁) that is inhomogeneous. In aninhomogeneous field, the measured NMR signal can be determined as afunction of both ω₁ and resonant frequency offset (Δω₀), as follows:

$\begin{matrix}{{{V_{x,y}(t)} \approx {\frac{2\chi}{\mu_{0}}{\int{\int{{f( {{\Delta\omega}_{0},\omega_{1}} )}{F( {\Delta\omega}_{0} )}{m_{x,y}( {{\Delta \; \omega_{0}},\omega_{1}} )}\omega_{RF}^{2}{{\Delta\omega}_{0}}{\omega_{1}}}}}}},} & {{Eq}.\mspace{14mu} 26}\end{matrix}$

where χ is the nuclear susceptibility, F(Δω₀) is the frequency responseof the detection system, m_(x,y)(Δω₀,ω₁) is the local transversemagnetization, and the function ƒ(Δω₀,ω₁) can be determined from B₀ andB₁ field maps, a spin density map of the sample, and a coil efficiencyfactor. In the presence of the B-S phase shift, Equation 26 can berewritten as:

$\begin{matrix}{{V_{x,y}(t)} \approx {\frac{2\chi}{\mu_{0}}{\int{\int{{\exp( \frac{\; \omega_{1}^{2}T_{BS}}{\Delta \; \omega_{RF}} )}{f( {{\Delta\omega}_{0},\omega_{1}} )}{F( {\Delta\omega}_{0} )}{m_{x,y}( {{\Delta \; \omega_{0}},\omega_{1}} )}\omega_{RF}^{2}{{\Delta\omega}_{0}}{\omega_{1}}}}}}} & {{Eq}.\mspace{14mu} 27}\end{matrix}$

Equation 27 above shows that the off-resonant pulses will change boththe shape of the echo, as well as the phase of the echo.

Illustrative embodiments of the present disclosure can also detectchanges within the applied oscillating field (B₁). Magnetic debris oftencauses significant changes in the static magnetic field distributionB₀({right arrow over (r)}) of NMR well-logging tools. As a result, thelocation and shape of the sensitive volume (shell) changes, leading tocalibration errors in basic NMR measurements such as porosity. Themulti-segment sequences can be combined with other measurements of B₁(for example, from a pickup loop) to detect such B₀ changes. The skindepth at the low Larmor frequencies used in well-logging is usuallysignificantly larger than the depth of investigation. Therefore, thedependence of B₁ on salinity is spatially uniform (e.g., can be modeledas a uniform scaling of B₁({right arrow over (r)}) by a factor α). Inparticular, the B₁ values measured by the multi-segment sequences (atthe sensitive volume) and the pickup loop (near the tool) scale by thesame factor as a function of salinity. Deviation from uniform scalingindicates that the location of the sensitive volume has changed. Theknown spatial dependence of B₁({right arrow over (r)}) can be used toestimate the magnitude and direction of this shift.

In the embodiments, described above, the shells are spatially separatedby using a difference in applied frequency between pulse sequencesegments. In additional or alternative embodiments, the shells can alsobe spatially separated by using different transmit and receive coils,and/or using the motion of the sample.

Various embodiments of such multi-segment sequences for determining theapplied oscillating field can be used in both medical and oilfieldapplications. The sequences can be used to calibrate the amplitudeand/or duration of applied RF pulses so that the pulses produce thedesired effect on nuclear spins. The calibration is repeatedperiodically because the magnetic field generated by a given pulse candepend significantly on the presence and properties of the sample. Forexample, the temperature of the sample may change over time and willhave an impact on the magnitude of the applied field. As a result, insome cases, RF pulse lengths in downhole NMR tools are adjusted by 20%or more as a function of temperature and coil quality factor (e.g.,which is a function of formation conductivity). Illustrative embodimentsof the multi-segment sequences advantageously determine the magnitude ofthe applied oscillating field quickly and accurately, as compared toconventional methods. For example, one conventional method, as describedabove, varies RF pulse durations and plots the NMR signal amplitude as afunction of pulse duration and determines peaks. This method is timeconsuming because it requires several NMR measurements (e.g.,acquisitions) to determine the peaks. In another example, an inductivepick up loop is used to measure the applied oscillating field. Such asystem, however, requires additional components, namely, the additionalinductive pick up loop. In addition, the system detects the oscillatingfield near the location of the loop, which does not usually coincidewith the NMR sensitive volume (shell).

Illustrative embodiments of the present disclosure are also directed toapplying multi-segment NMR sequences to different sets of atomic nuclei.Such an NMR pulse sequence includes at least a first pulse sequencesegment at a first set of frequencies applied to a first set of atomicnuclei, such as carbon nuclei, and a second pulse sequence segment at asecond set of frequencies applied to a second set of atomic nuclei, suchas sodium nuclei. The second pulse sequence segment is initiated beforethe first set of atomic nuclei reach thermal equilibrium. In someembodiments, the segments are interposed within each other, as describedabove. In some cases, the first set of atomic nuclei and the second setof atomic nuclei are from different chemical species (e.g., differentatoms, ions or molecules). In other cases, the first set of atomicnuclei and the second set of atomic nuclei are from the same chemicalspecies.

In some embodiments, more than two sets of atomic nuclei areinvestigated within the same shell using two or more pulse sequencesegments. The set of atomic nuclei can be one or more of hydrogen (e.g.,¹H protons, ²H deuterium), fluorine (e.g., ¹⁹F), sodium (e.g., ²³Na),and carbon (e.g., ¹³C). Table 2 below shows various properties for eachnucleus.

TABLE 2 Nucleus ¹H ²H ¹⁹F ²³Na ¹³C Spin, I 1/2 1 1/2 3/2 1/2Gyromagnetic ratio, γ 4.26 0.654 4.01 1.127 1.071 (kHz/G) Naturalabundance 99.985% 0.015% 100% 100% 1.1% Quadrupole moment (mb) 0 2.86 0100.6 0

The frequency for each pulse sequence segment is selected so thatsegment produces resonant signals within a specific set of atomicnuclei. To this end, the pulse sequence segments are selected to matchthe Larmor frequency of a specific set of nuclei. The Larmor frequency(ω₀) for a specific set of nuclei can be determined from the magnitudeof the static magnetic field (B₀) and the gyromagnetic ratio (γ) of theset of nuclei (e.g., ω₀=γB₀). The gyromagnetic ratios for several nucleiare shown above in Table 2.

In illustrative embodiments, the pulse sequence segments are applied toa substance and the nuclei within the substance using a broadband NMRsystem, as further described below. The system can advantageouslymeasure NMR signals from multiple nuclei at different Larmor frequenciesin parallel and without physical changes in the hardware. Furthermore,by using a broadband system, the amplitude of the oscillating (RF)magnetic field is inversely proportional to its frequency (e.g.,B₁∝1/ω_(RF)) and, in addition, is near resonance (e.g., ω_(RF)≈ω₀).Thus, the sequence pulse lengths (T) at any given position in the sample(implying a fixed value of B₀) are invariant with the gyromagnetic ratio(γ) of the atomic nuclei, as shown below:

$\begin{matrix}{{T \propto \frac{1}{\omega_{1}}} = {{\frac{1}{\gamma \; \beta_{1}} \propto \frac{1}{\gamma ( \frac{1}{\omega_{RF}} )} \approx \frac{1}{\gamma ( \frac{1}{\omega_{0}} )}} = {\frac{1}{\gamma ( \frac{1}{\gamma \; B_{0}} )} = B_{0}}}} & {{Eq}.\mspace{14mu} 28}\end{matrix}$

Accordingly, in some embodiments, an appropriate pulse length can bedetermined for the first set of atomic nuclei and similar pulse lengthscan be used for other sets of atomic nuclei. For example, pulse lengthsdetermined for sensitive nuclei (such as ¹H) can be reused forless-sensitive nuclei (such as ¹³C), and do not have to be determinedagain. This saves considerable measurement time. Thus, the variousdifferent pulse segments can advantageously have pulses with similarlengths (T).

When the NMR system applies a pulse sequence segment having a particularfrequency (e.g., over a limited bandwidth), the thickness of the shellwill be inversely proportional to gyromagnetic ratio of the nucleiwithin the substance. This behavior occurs because the coil current andB₁ amplitude of the NMR system is inversely proportional to the Larmorfrequency (e.g., B₁∝1/w_(RF)). In one particular embodiment, thegradient (g_(z)=|dB₀/dz|) of the static field within the shell increaseslinearly with the static field, that is, g_(z)∝B₀. In this case, wehave:

$\begin{matrix}{{{{B_{1} \propto \frac{1}{\omega_{0}}} = \frac{1}{\gamma \; B_{0}}},{g_{z} \propto B_{0}}}{{\Delta \; z} \approx \frac{2B_{1}}{g_{z}} \propto {\frac{1}{\gamma \; B_{0}^{2}}.}}} & {{Eq}.\mspace{14mu} 29}\end{matrix}$

where Δz is the shell thickness. Due to the relationship in Equation 29,signal amplitude of the resonant signal (in voltage units) scales as:

γ³ I(I+1)B ₀ ² Δz∝I(I+1)γ²  Eq. 30

where I is the spin of the atomic nucleus. The number of signal averages(e.g., scans) used to obtain a given SNR in voltage units scales as:

$\begin{matrix}{N \propto \frac{1}{{I^{2}( {I + 1} )}^{2}\gamma^{4}}} & {{Eq}.\mspace{14mu} 31}\end{matrix}$

where N is the number of signal averages.

FIGS. 29 and 30 show measured asymptotic CPMG echoes for a sodium sample(250 ppK NaCl (brine)) and a deuterium sample (40% D₂O, 60% H₂O (heavywater doped with NiCl₂)), respectively. FIGS. 29 and 30 were produced bysumming the echoes within the resonant signal from each sample. Data wastaken at multiple Larmor frequencies with various pulse sequences. Theresults match spin dynamics simulations well. Additional CPMGmeasurements (not shown) were used to estimate T₂ for these samples. Thesodium sample had a proton relaxation time of 2 seconds (T_(2H)≈2 s) anda sodium relaxation time that was much shorter (T_(2Na)=42 ms). Thesodium relaxation time case was dominated by quadrupolar interactions.On the other hand, the deuterium sample had a proton relaxation time ofT_(2H)=200 ms and a deuterium relaxation time that was substantiallylonger (T_(2D)=420 ms). This longer relaxation time occurs in spite ofthe fact that ²H is quadrupolar (I=1). There are two reasons for thislonger relaxation time. Firstly, the quadrupolar moment of ²H is small,resulting in little quadrupolar relaxation. Secondly, protons haveenhanced dipolar relaxation relative to deuterons. In this sample,dipolar relaxation is dominated by interactions between target nucleiand unpaired electrons within paramagnetic ions in solution. As aresult, both longitudinal and transverse relaxation rates areproportional to the square of the nuclear gyromagnetic ratio:

$\begin{matrix}{{R_{1} = {\frac{1}{T_{1}} \propto {{I( {I + 1} )}( {\gamma_{n}\gamma_{e}} )^{2}}}},{R_{2} = {\frac{1}{T_{2}} \propto {{I( {I + 1} )}{( {\gamma_{n}\gamma_{e}} )^{2}.}}}}} & {{Eq}.\mspace{14mu} 32}\end{matrix}$

where γ_(n) and γ_(e) are the nuclear and electronic gyromagneticratios, respectively, and I is the nuclear spin. The significantlyhigher gyromagnetic ratio of protons relative to deuterons results inenhanced dipolar relaxation for the proton nucleus. FIGS. 29 and 30 weregenerated using a broadband NMR system. The broadband NMR system appliedpulse sequences with rectangular 90 degree excitation pulses andrectangular 135 degree refocusing pulses. The sequence and sampleparameters for FIG. 29 included T_(E)=800 μs/900 μs; T_(acg)=262 μs;T_(R)=200 ms; and N=16384, where T_(E) is the echo spacing, T_(acq) isthe acquisition time, T_(R) is the time between repetitions of thesequences, and N is the number of times the sequences are repeated. Thesequence and sample parameters for FIG. 30 included ω₀=2π×342 kHz;T_(E)=1 ms; T_(acg)=262 μs, T_(R)=1.0 s, and N=1024.

Illustrative embodiments of the present invention are also directed todepth profiling of multiple nuclei. FIG. 31 shows the measured protonand sodium depth profiles of a brine sample. The wait times betweensuccessive scans can be kept short (e.g., less than 200 ms) formeasuring sodium nuclei because sodium nuclei have short T₁ times. As aresult, the sodium profile can be measured relatively quickly (e.g.,only 2.5 times slower than the proton profile, in this case). Suchsodium profiles can be used to estimate the brine content in a mixtureof oil and brine as a function of radial distance from the tool (depth)during NMR well logging. Such a measurement can be referred to as an“NMR salinity log.” FIG. 31 shows a multi-nuclear depth profile that wasgenerated using a broadband system. In particular, FIG. 31 shows anormalized proton and sodium depth profiles of a 250 ppK brine solutionlocated at a center frequency of 2.0 MHz for the proton nuclei and 529kHz for the sodium nuclei. The experimental time required to acquireeach point in the profiles was 64 seconds (proton, N=16) and 150 seconds(sodium, N=1024).

Illustrative embodiments of the present disclosure use broadband NMRelectronics to apply multi-segment sequences at different frequenciesand/or to detect resonant signals at different frequencies. Conventionalnarrowband NMR electronics can switch frequencies at the end of acomplete pulse sequence, such as a CPMG sequence. To switch betweenfrequencies, such conventional narrowband systems use banks of fixedcapacitors and mechanical switches that are coupled to a coil. Themechanical switches tune the coil to different frequencies by switchingbetween a pre-set number of fixed capacitors. Such narrowband systemssuffer from several disadvantages. Firstly, the switches within thecapacitor banks introduce noise into the NMR measurement. Secondly, apredetermined discrete set of narrowband frequencies can be set becauseeach frequency is dependent on a separate capacitor. Thirdly, thefrequency switching process introduces dynamics and may not maintainphase coherence of the pulse sequence waveform. Fourthly, the switchingprocess is slow (e.g., 10-100 ms switching times).

Exemplary embodiments presented herein avoid such problems. BroadbandNMR electronics can switch between frequencies that are outside anatural resonant frequency bandwidth of a coil with a tuned circuit. Inother words, broadband electronics do not depend on tuning a coil to seta particular frequency. In contrast to conventional narrowband systems,which use mechanical switches and banks of fixed capacitors to tune thecoil, various embodiments of the broadband electronics described hereinachieve multi-frequency operation without a need for hardware modulation(e.g., switching between fixed capacitors or tuning between variablecapacitors). In this manner, the broadband electronics are frequencyinsensitive and allow the pulse sequence frequency to be dynamicallyvaried by a spectrometer while maintaining phase coherence of an outputwaveform.

As explained above, in some cases, the broadband NMR electronics canswitch between frequencies with a frequency difference (Δw_(RF)) asgreat as 10% of an initial applied frequency. In various otherembodiments, the frequency can be even greater (e.g., 20% 30% or 50%).Also, in some embodiments, the broadband NMR electronics can switchbetween frequencies in less than 5 μs. In yet further embodiments, thebroadband NMR electronics can switch between frequencies in less than 20μs or 50 μs. Furthermore, in some embodiments, the broadband NMRelectronics can operate within a frequency range of 100 kHz and 3.2 MHz.

FIG. 32A shows broadband NMR device 3200 in accordance with oneembodiment of the present disclosure. The broadband NMR device 3200includes a coil 3202 that is coupled to broadband NMR electronics 3204,3206, 3208. A sample substance is located inside and/or outside of thecoil 3202. The broadband NMR electronics include a broadband transmitter3204 and a broadband receiver 3206. Each of the transmitter 3204 and thereceiver 3206 are coupled to the coil 3202.

The broadband NMR transmitter 3204 includes a non-resonant NMRtransmitter circuit 3210 that is coupled to the coil 3202. Thetransmitter circuit 3204 is “non-resonant” because the resonantfrequency of the circuit does not need to match the Larmor frequency ofinterest. In contrast, as explained above, conventional circuits settheir resonant frequencies to match the Larmor frequency of interest byselecting a particular capacitance for the circuit. Although thenon-resonant transmitter circuit 3210 and coil 3202 may use capacitorsand have some associated capacitance, this capacitance is notspecifically selected to match a Larmor frequency of interest. FIG. 32Bshows a non-resonant NMR transmitter circuit 3210 in accordance with onespecific embodiment of the present disclosure. In this specific example,the NMR transmitter circuit 3210 includes a set of four switches: A3212, B 3214, C 3216 and D 3218. These switches control the timing andthe direction of the current flow in the coil. Turning these switches onand off using a certain switching logic generates an alternating currentin the coil and thus produces RF irradiation. The switching logic oftenincludes a period of positive current followed by a period of negativecurrent, simulating a sinusoidal waveform. Repeating this pattern at agiven frequency allows the generation of RF power at a particularfrequency. In one particular embodiment, the switches 3212, 3214, 3216,3218 are transistors, such as metal-oxide-semiconductor field-effecttransistors (MOSFET), insulated gate bi-polar transistors (IGBT), orvarious other switches based upon the high frequency switching (HFS)family. In various embodiments, the switches can switch at less than 10ns. The switches 3212, 3214, 3216, 3218 are arranged in a circuit 3220known as an H-bridge, as shown in FIG. 32B. In one embodiment, theswitches 3212, 3214, 3216, 3218 are controlled by two non-overlappingdigital signals denoted as φ₁ and φ₂ 3222, 3224. The signals φ₁ and φ₂3222, 3224 include a switching logic, which is used to drive the twosets of switches, (A and D) and (B and C), such that a voltage sourceV_(batt) 3226 is connected with alternating polarity across the coil3202 and an oscillatory coil current (I₁) is created. A load resistor R₁3228 or fuse can be used in series with the voltage source to limit thecurrent that is applied to the switches 3212, 3214, 3216, 3218. Thedigital signals denoted as φ₁ and φ₂ 3222, 3224 are used to control theswitches 3212, 3214, 3216, 3218 and a desired frequency of an NMRsequence (e.g., a multi-segment sequence) is achieved by repeating thesesignals at the desired frequency. In some embodiments, other digitalsignals can be used to control each of the switches 3212, 3214, 3216,3218 individually. For example, the signals may include high components(e.g., φ_(1H) and φ_(2H)) that control the high-side switches 3212, 3214and low components (e.g., φ_(1L) and φ_(2L)) that control the low-sideswitches 3216, 3218.

The broadband NMR transmitter 3204 also includes a driver 3230 that iscoupled to the non-resonant NMR transmitter circuit 3210. In oneparticular embodiment, the driver 3230 can be a computer processor. Thedriver 3230 is used to control the switches 3212, 3214, 3216, 3218within the transmitter circuit 3210. The driver 3230 switches theswitches 3210 according to the switching logic within the digitalsignals (e.g., φ₁ and φ₂). In various embodiments, the driver 3230 alsoreceives NMR pulse sequences from an NMR spectrometer 3208. In someembodiments, the NMR pulse sequences are sent along a plurality ofchannels. An adder circuit (not shown) can be used to combine theplurality of channels. Also, in various embodiments, the transmitter3204 includes a comparator 3231 for receiving the NMR pulse sequencesfrom the spectrometer 3208 and generating a square waveform that is thenprovided to the driver 3230. The NMR pulse sequences can be translatedby the driver 3230 into the particular switching logic by selectingpositive and negative waveforms of the NMR pulse sequences and thenconditioning the waveforms to an appropriate voltage. In this manner,modulating hardware, such as a tuning capacitor, is not necessary inorder to achieve a particular frequency. Instead, the frequency ismodulated directly by the spectrometer 3208.

The coil 3202 is also coupled to the broadband NMR receiver 3204 so thatNMR resonant signals can be detected within the sample. The coil 3202 iscoupled to the broadband receiver 3206 using a duplexer 3232. Theduplexer 3232 decouples the receiver 3206 from the coil 3202 when thecoil is operating in a transmitting mode (e.g., transmitting an NMRpulse sequence). In this manner, the duplexer 3232 protects the receiver3206 during a transmitting mode. In one particular embodiment, theduplexer 3232 includes switches and a switch driver 3234 that opens theswitches during a transmitting mode and closes the switches during areceiving mode of operation. In various embodiments, the duplexer 3232includes two back-to-back field effect transistors (FETs) that arecontrolled by an isolated driver circuit. This configuration produces abidirectional and broadband switch. The switch is bidirectional becausethe state of the switch is independent of the polarity of the voltage onthe coil. For example, such a switch will remain OFF regardless ofwhether the voltage across the coil is positive or negative. The switchis broadband because a reference voltage for the driver is not connectedto the same ground terminal as the remainder of the driver circuit.Control signals can be passed to the switch using various isolatedsignal transmission methods, such as magnetic transmission methods(e.g., using a transformer) or optical transmission methods (e.g., usingan optoisolator). In some embodiments, a duplexer is not used when thedevice 3200 includes separate transmit and receive coils.

FIG. 32C shows the broadband NMR receiver 3206 in more detail. Thebroadband NMR receiver can receive and process resonant NMR signals overa broad frequency range. In some embodiments, the ratio of the highestoperating frequency and lowest operating frequency is greater than 5. Invarious embodiments, this ratio is as great as 30 or 50. The highestoperating frequency and lowest operating frequency are defined by thefrequency range over which the performance of the receiver issatisfactory for its application. For example, in one case, thefrequency range is the range over which the input-referred noise of thereceiver is less than that of a 1-Ω resistor. This level of noise isconsidered adequate for NMR coils with resistance of 1Ω or larger. Invarious embodiments, the frequency range satisfying this condition is 3MHz to 0.1 MHz

Various embodiments of the broadband NMR receiver 3206 include atransformer 3236 that receives the NMR resonant signal from the coil3202 and amplifies the signal by proving a voltage gain. In someembodiments, the transformer is directly coupled to the duplexer 3232.The transformer 3236 may be a step-up transformer with a turn ratio of1:N. The turn ratio may be in the range of 1:2 to 1:10. For lowfrequency operation (e.g., below 5 MHz), the transformer 3236 mayinclude a soft magnetic core to increase the inductance and performanceof the transformer. However, in some embodiments, higher turn ratios canalso be used. For higher frequency operation (e.g., above 5 MHz), atransformer 3236 without a magnetic core can be used. In illustrativeembodiments, the transformer 3236 includes a low insertion loss and abandwidth that significantly exceeds the highest operating frequency ofthe receiver 3206. In some embodiments, for transformers 3236 withmagnetic cores, a magnetic shield may be installed around thetransformer. The shield reduces the magnetic field projected from theNMR magnet into the transformer 3236, which improves the performance ofthe transformer.

The receiver 3206 also includes a preamplifier 3238 that follows thetransformer 3236. In some embodiments, the preamplifier is directlycoupled to the transformer 3236. The transformer 3236 provides abroadband passive and low-noise voltage gain of a NMR signal that isdetected at the coil 3202. This voltage gain occurs before thepreamplifier 3238. In some cases, such a transformer-coupled topologyresults in a low noise figure (NF) over a wide frequency range. In onespecific example, the transformer 3236 has a turn ratio of 1:10 toamplify an input signal above a noise floor of the preamplifier 3238.Such a configuration can produce a low input-referred noise atfrequencies up to 10 MHz (e.g., 0.1 nV/Hz^(1/2), which is equal to thethermal noise produced by a 0.6Ω resistor at 300 K). After thetransformer, the NMR signal is passed to the preamplifier 3238, whichfurther amplifies the NMR signal.

The preamplifier 3238 includes a common-drain amplifier stage 3251 and acommon-source amplifier stage 3253. In FIG. 32C, the common-drainamplifier stage 3251 includes a transistor (J₁) that is configured as acommon-drain amplifier. The transistor (J₁) has an input signal fed atthe gate of the transistor and an output signal taken from the source ofthe transistor (e.g., also known as a source follower). In one specificembodiment, the transistor (J₁) is a junction gate field-effecttransistor (JFET). A gate-source capacitance (C_(gs)) and a gate-draincapacitance (C_(gd)) are intrinsic to the transistor (J₁). Byconfiguring the transistor (J₁) as a source follower, the preamplifier3238 advantageously applies the gate-drain capacitance (C_(gd)) at aninput terminal of the transistor. The gate-drain capacitance (C_(gd)) ismuch smaller than the gate-source capacitance (C_(gs)) when thetransistor (J₁) is biased in its usual region of operation (e.g., knownas saturation). The maximum RF frequency that can be amplified by thepreamplifier 3238 with low noise (e.g., useful bandwidth of thepreamplifier) is proportional to:

1/√{square root over (C _(input))},  Eq. 33

where C_(input) is the total capacitance at the input of the transistor(J₁). The transistor (J₁) contributes a significant portion of totalcapacitance at the input of the transistor (C_(input)) so reducing itscontribution from h gate-source capacitance (C_(gs)) to the gate-draincapacitance (C_(gd)) significantly increases the bandwidth of thepreamplifier.

In FIG. 32C, a single transistor is shown within the common-drainamplifier stage 3251 of the preamplifier 3238. In other embodiments,however, the common-drain amplifier stage 3251 can include a pluralityof common-drain amplifiers that are, for example, coupled in parallel(e.g., a plurality of transistors configured as source followers andcoupled in parallel).

Once the NMR signal passes the common-drain amplifier stage 3251, theNMR signal is further amplified by the common-source amplifier stage3253, which provides a voltage gain to the signal. In the embodimentshown in FIG. 32C, the common-source amplifier stage includes 3253 anumber (M) of transistors that are coupled in parallel. In someembodiments, the number of transistors (M) can be between 2 and 10. Thecommon-source stage 3253 reduces the noise that the stage contributes toa level that is 1/M times that contributed by the common-drain amplifierstage 3251 (in power units). By making M much larger than 1, the noisecontributed by the stage can be reduced, thus minimizing the noise floorof the preamplifier 3238.

The examples above use JFETs (e.g., as J₁ and as J₂), however, othertypes of transistors can also be used, such as bipolar junctiontransistors (BJT) and/or metal oxide field effect transistors (MOSFET).In various embodiments, the transistors have low current and voltagenoise, and also include small capacitances between their terminals.

FIG. 32D shows another embodiment of a preamplifier 3241 that can beused with the NMR receiver 3206. The preamplifier 3238 of FIG. 32C usesa resistor (R_(S)) at the source of the transistor (J₁) to set a DC biascurrent through the transistor. A negative power supply (V_(SS)) isapplied at an end of the resistor (R_(S)) because of a DC voltage dropacross the resistor. In one specific embodiment, the resistor is 820Ωand the power supply is −5 V. In contrast to the preamplifier 3238 ofFIG. 32C, the preamplifier 3241 of FIG. 32D replaces the resistor(R_(S)) with a large inductor (L_(S)) that is coupled to the transistor(J₁). In one specific embodiment, the inductor has an inductance of 470μl. By using such an arrangement, the preamplifier 3241 of FIG. 32D canomit the use of the power supply (V_(SS)).

FIG. 32E shows yet another embodiment of a preamplifier 3243 that can beused with the NMR receiver 3206. In this embodiment, the preamplifier3243 includes a second transformer that is coupled between thecommon-drain amplifier stage 3251 and the common-source amplifier stage3253. The second transformer amplifies the NMR signal by providing avoltage gain to the signal. In some embodiments, the voltage gainprovided by the transformer is substantially noiseless. The transformermay be step-up transformer with a turns ratio of 1:M (e.g., between 1:2and 1:10). In some embodiments, the second transformer includes amagnetic core, while, in other embodiments, a core is not used. If amagnetic core is used, then the transformer may be enclosed with amagnetic shield. The shield prevents the magnetic field of the NMRmagnet from penetrating the transformer core.

This second transformer is followed by the common-source amplifier stage3253. In this specific embodiment, the common-source amplifier stage3253 includes a single transistor (J₂) configured as a common-sourceamplifier. Other embodiments, however, may include additionaltransistors. The second transformer reduces the noise contributed by thecommon-source amplifier stage 3253 to a level that is 1/M² times thatcontributed by the common drain amplifier stage 3251 (in power units).Thus, the noise contribution of the common-source amplifier stage 3253and later stages can be made insignificant for relatively small valuesof M, and, in this manner, the configuration creates a very low-noisepreamplifier. For example, in an embodiment where M is 4, the totalinput-referred noise of the preamplifier is only 6.25% larger than thatof the common drain amplifier stage alone. In various embodiments, thepreamplifier 3243 also advantageously saves a significant amount ofpower. In particular, the resistor or the inductor at the transistor(J₁) can be omitted because the primary side of the second transformersets the DC bias point for the transistor (J₁) and the secondary side ofthe transformer does not need to consume DC power.

In various embodiments, the preamplifiers 3238, 3241, 3243 describedherein have increased bandwidth (e.g., over 3 MHz for a typical NMR coilof inductance 15 μH), improved settling time, and similar input-referrednoise, as compared to conventional preamplifiers. One conventionalexample of a transformer-coupled preamplifier for low frequencyoperation (e.g., less than 50 kHz) is the SR-554, which can be obtainedfrom Stanford Research Systems™.

As shown in FIG. 32C, the broadband receiver 3206 includes a DC blockingnetwork 3247 that is disposed after the preamplifier 3238. The DCblocking network 3247 sets an output (V_(out)) of the preamplifier 3238to ground, which maximizes the overall dynamic range of the receiver3206.

In the specific embodiment of FIG. 32C, the broadband receiver 3206 alsoincludes a feedback network 3245. The feedback network is coupled to thepreamplifier 3238 and configured to reduce settling time of thepreamplifier. In this case, the feedback network is coupled to an input(V_(in)) of the preamplifier 3238 at one end and after the DC blockingnetwork 3247 at the other end. The feedback network 3245 removesunwanted high-frequency resonances between inductive impedance at theNMR coil 3202 and capacitive input impedance (C_(input)) at thepreamplifier 3238. These resonances are produced by RF pulses that areapplied to the coil 3202 by the transmitter 3204 and can adverselyaffect the settling time of the receiver 3206. To reduce the settlingtime, without adding noise, the particular feedback network 3245 shownin FIG. 32C uses an op-amp based integrator circuit followed by a smallfeedback capacitor (C_(f)). The feedback network 3245 produces anoiseless damping resistance (R_(damp)) between the input of thepreamplifier (V_(in)) and ground to remove these resonances. Thenoiseless damping resistance (R_(damp)) can be defined by:

R _(damp)=τ/(AC _(f)),  Eq. 34

where τ=R₁C₁ is the time constant of the integrator circuit, and A isthe overall voltage gain of the preamplifier. Other types of feedbacknetworks can also be used. For example, a feedback resistor (R_(f)) canreplace the capacitor (C_(f)) and a voltage gain circuit can replace theintegrator circuit.

In various embodiments, the settling time of the receiver can be furtherimproved by limiting the signal amplitude at various locations withinthe receiver 3206 using diode clamps. In the embodiment shown in FIG.32C, a diode clamp 3249 is coupled between the transformer 3236 and theinput (V_(in)) of the preamplifier 3238 (e.g., at the gate of thetransistor (J1)). The diode clamp 3249 includes a pair of cross-coupleddiodes that limit maximum signal amplitude across the diodes toapproximately a threshold voltage of each diode (V_(on)). Typical valuesof the threshold voltage (V_(on)) for silicon diodes range from 0.6 V to0.7 V. Similar diode clamps can also be used at other locations withinthe receiver 3206, such as after the output (V_(out)) of thepreamplifier and/or between the common-drain stage (J1) andcommon-source stage (J2).

The broadband NMR electronics 3204, 3206, 3208 also include aspectrometer 3208. In some embodiments, the output of the preamplifier3238 is passed through further stages of analog filtering before beingsent to the spectrometer 3208. For example, high-pass and low-passfilters can set the minimum and maximum detectable NMR frequency,respectively. The cutoff frequencies of these filters can be variedbased on the application.

In some embodiments, the detected resonant signal is output by thebroadband receiver 3238 in analog form. In such embodiments, thespectrometer 3208 may include a digitizer 3240 for converting thedetected resonant signal into digital data. Furthermore, in variousembodiments, demodulation of the NMR signal can occur within thespectrometer 3208. In various other or alternative embodiments, however,demodulation of the NMR signal can also occur within the broadband NMRreceiver 3206. The spectrometer 3208 also includes a post-processor 3242that is used to interpret the detected digital resonant data and todetermine NMR properties from the detected data. This data can bepresented to a user using an operator module 3244 with a graphical userinterface (GUI). In various embodiments of the present disclosure, theoperator interface 3244 and the GUI are not part of the broadband NMRelectronics 3204, 3206, 3208. The spectrometer 3208 also includes apulse sequence generator 3246. The pulse sequence generator 3246generates NMR sequences based upon parameters selected by an operator atthe operator module 3244. The pulse sequence generator 3246 provides thesequences to the transmitter 3204. In one particular embodiment, thespectrometer 3208 is a Kea™, which can be obtained from Magritek™. Thespectrometer 3208 can be controlled from the operator module 3244 usingProspa™ software, which can also be obtained from Magritek™.

Further details of broadband NMR electronics (e.g., non-resonant NMRsystems) are described in U.S. Publication No. 2012/0001629 published onJan. 5, 2012.

FIG. 33 shows a broadband NMR system 3300 for applying multi-segmentsequences to a substance 3302 in accordance with one embodiment of thepresent disclosure. The system 3300 includes an NMR module 3304. Invarious embodiments, the NMR module 3304 includes an electro-magneticdevice 3306 for applying a static magnetic field to the substance 3302.In some embodiments, the electro-magnetic device 3306 is a magnet or anarray of magnets. The magnets can be formed from a samarium-cobalt(SmCo) magnetic material.

The NMR module 3304 also includes at least one coil (e.g., antenna) 3308and broadband NMR electronics 3310 electronically coupled to the coil.The coil 3308 and broadband NMR electronics 3310 apply an oscillatingfield to the substance 3302 (e.g., a radio frequency (RF) field). Inaccordance with exemplary embodiments of the present disclosure, theoscillating field applied to the substance includes a multi-segmentsequence, such as a sequence with interposed pulse sequence segments.The coil 3308 and broadband NMR electronics 3310 are also used to detectresonant signal that originate within the substance 3302.

The broadband NMR electronics 3310 are electronically coupled to aprocessor 3312 and a memory 3314 (e.g., a computer system). The memory3314 can be used to store computer instructions (e.g., computer programcode) that are interpreted and executed by the processor 3312. Thememory 3314 may be a digital memory such as a random-access memory, aflash drive, a hard drive or a disc drive.

In alternative or additional embodiments, the multi-segment sequencesdescribed herein may be implemented as a series of computer instructionsfixed either on a non-transitory tangible medium, such as a computerreadable medium (e.g., a diskette, CD-ROM, ROM, field-programmable array(FPGA) or fixed disk) or transmittable to a computer system, via a modemor other interface device, such as a communications adapter connected toa network over a tangible medium (e.g., optical or analog communicationslines). The series of computer instructions can embody all or part ofthe multi-segment sequences described herein.

The multi-segment sequences described herein and various other NMR pulsesequences may be stored within the memory 3314 as software or firmware.The processor 3312 may be configured to retrieve the sequences frommemory 3314 and provide instructions to the broadband NMR electronics3310 to apply the sequences to the substance 3302. The detected resonantsignals may also be communicated from the broadband electronics 3310 tothe processor 3312 for storage on the memory 3314.

The processor 3312 is also electronically coupled to a communicationsmodule 3316. The communications module 3316 communicates with anoperator module 3318. The operator module 3318 also includes acommunications module 3320 so that the operator module 3318 cancommunicate with the NMR module 3304. A communications link 3322 betweenthe operator module 3318 and the NMR module 3304 can be establishedusing, for example, a hard-wired link, an optical link, acoustic link,and/or a wireless link. The operator module 3318 includes a processor3324 and a memory 3326 (e.g., a computer system). The processor 3324 andmemory 3326 support a graphical user interface (GUI) 3328, such as amonitor, a touch screen, a mouse, a keyboard and/or a joystick. The GUI3328 allows an operator to control and communicate with the NMR module3304. The processor 3324 is also electronically coupled to one or moreinformation input devices 3330. In some embodiments, the input device3330 is a port for communicating with a removable medium (e.g., adiskette, CD-ROM, ROM, USB and/or fixed disk). In additional oralternative embodiments, the input device 3330 is a modem and/or otherinterface device that is in communication with a computer network (e.g.,Internet and/or LAN). In various embodiments, the NMR module 3304 andthe operator module 3318 can be used to perform functions selected fromthe following non-limiting list:

-   -   Communicate instructions to the NMR module 3304 to initiate        and/or terminate NMR measurements;    -   Communicate instructions to change parameters of NMR sequences        to the NMR module 3304 (e.g., pulse amplitude of sequences,        pulse lengths, timing between pulses, shape of pulses, and/or        frequency of pulses);    -   Communicate detected NMR signal data from the NMR module 3304 to        the operator module 3318;    -   Communicate NMR pulse sequences from the operator module 3318 to        the NMR module 3304;    -   Perform analysis of detected NMR signal data to determine NMR        properties of substances at the operator module 3318 and/or the        NMR module 3304;    -   Display various plots of NMR properties to the operator at the        operator module 3318; and    -   Download NMR pulse sequences from the operator module 3318 to        the NMR module 3304.

Illustrative embodiments of the present disclosure are not limited tothe system shown 3300 in FIG. 33. Various modifications can be made tothe system 3300. For example, in one specific embodiment, the NMR module3304 lacks the processor 3312 and the memory 3314. In such anembodiment, the processor 3324 and memory 3326 on the operator side 3318support the broadband NMR electronics 3310. Furthermore, in someembodiments, the NMR module 3304 and the operator module 3318 can bephysically located in two separate locations. For example, in a boreholeapplication, the NMR module 3304 can be located downhole, while theoperator module 3318 is located at the surface. In various otherembodiments, the NMR module 3304 and the operator module 3318 can bephysically located in the same place as a single system. This may be thecase when the system is used in a surface environment such as alaboratory.

Illustrative embodiments of the present disclosure are further directedto oil and gas field applications. FIG. 34 shows a wireline system 3400for applying multi-segment sequences to a substance 3402 in accordancewith one embodiment of the present disclosure. The wireline system 3400is used to investigate, in situ, a substance 3402 within an earthformation 3404 surrounding a borehole 3406 to determine a characteristicof the substance (e.g., characteristics of solids and liquids within theearth formation). As shown in FIG. 34, a wireline tool 3408 is disposedwithin the borehole 3406 and suspended on an armored cable 3410. Alength of the cable 3410 determines the depth of the wireline tool 3408within the borehole 3406. The length of cable is controlled by amechanism at the surface, such as a drum and winch system 3412. Althoughthe wireline tool 3408 is shown as a single body in FIG. 34, the toolmay alternatively include separate bodies.

As shown in FIG. 34, the wireline tool 3408 includes an NMR loggingmodule 3414 that is used to apply multi-segment sequences. The NMRlogging module 3414 includes a face 3416 that is shaped to contact theborehole wall 3406 with minimal gaps or standoff. In some embodiments, aretractable arm 3418 is used to press the body of the wireline tool 3408and the face 3416 against the borehole wall 3406. The NMR logging module3414 also includes an electro-magnetic device 3420 for applying a staticmagnetic field to a sensitivity zone 3422 within the earth formation3404. As explained above, in some embodiments, the electro-magneticdevice 3420 is a magnet or an array of magnets formed from a magneticmaterial.

The NMR logging module 3414 also includes at least one coil 3424 andbroadband NMR electronics 3426 electronically coupled to the coil. Thecoil 3424 and broadband NMR electronics 3426 apply an oscillating fieldto an area of interest 3428 within the earth formation 3404. The area ofinterest 3402 is located within the sensitivity zone 3422 of theelectro-magnetic device 3420. In accordance with exemplary embodimentsof the present disclosure, the oscillating field applied to the earthformation 3404 includes multi-segment sequences, such as the interposedsequences described above. The static magnetic field and oscillatingfield generate resonant signals within the area of interest 3428. Theseresonant signals are detected by the coil 3424. The detected resonantsignals are used to determine characteristics of the substance 3402within the area of interest 3428.

The wireline system 3400 includes surface equipment 3430 for supportingthe wireline tool 3408 within the borehole 3406. In various embodiments,the surface equipment 3430 includes a power supply for providingelectrical power to the wireline tool 3408. The surface equipment 3430also includes an operator interface for communicating with the NMRlogging module 3414. Such an operator interface has already beendescribed with reference to FIG. 33. In some embodiments, the NMRlogging module 3414 and operator module communicate through the armoredcable 3410.

FIG. 35 shows another wireline system 3500 for applying multi-segmentsequences to a substance 3502 in accordance with one embodiment of thepresent disclosure. In contrast to FIG. 34, which shows an embodimentwhere the area of interest 3428 is outside of the coil 3424, FIG. 35shows an illustrative embodiment where the coil 3506 is used to analyzesubstances located within the coil. To this end, the wireline system3500 includes a flow line NMR module 3508. The flow line NMR module 3508includes a flow line (or chamber) 3510 that is at least partiallydisposed within the coil 3506. The area of the flow line 3510 disposedwithin the coil 3506 is defined as an area of interest 3504. Anelectro-magnetic device 3512, such as a magnet or a coil, can be used toapply a static magnetic field to the area of interest 3504. A probemodule 3514 is used to probe an earth formation 3516. A formation fluidis pumped into the flow line 3510 from the probe module 3514. Theformation fluid (e.g., substance) flows through the flow line 3510 andinto the area of interest 3504 where the formation fluid is analyzedusing a multi-segment sequence applied by the coil 3506 and broadbandNMR electronics 3518. In an alternative or additional embodiment, theformation fluid is passed to a separate chamber that is disposed withinthe coil and the formation fluid is analyzed within the separatechamber. Once the analysis is performed, in some embodiments, theformation fluid flows to a pump-out module 3520 that expels theformation fluid from the flow line 3510.

Illustrative embodiments of the present disclosure can also be appliedin logging-while-drilling (LWD) systems. FIG. 36 shows a LWD system 3600for applying multi-segment sequences to a substance in accordance withone embodiment of the present disclosure. The LWD system 3600 can beused to investigate, in situ, a substance 3602 within an earth formation3604 surrounding a borehole 3606 to determine a characteristic of thesubstance, while a drilling operation is performed. The LWD system 3600includes a drill string 3608 that is suspended within the borehole. Thedrill string 3608 includes a drill collar 3610 with a drill bit 3612disposed at the lower-end of the drill collar. The LWD system 3600 alsoincludes a surface system with a derrick assembly and platform assembly3614 positioned over the borehole 3606. The derrick assembly 3614rotates the drill string 3608 and, as the drill string rotates, thedrill bit 3612 drills deeper into the borehole 3606. An LWD NMR loggingmodule 3616 is disposed within the drill collar 3610 so that the modulecan log the surrounding earth formation as the drilling operation isperformed. The logging module 3616 communicates with surface equipment3618, which includes an operator interface for communicating with themodule. Such an operator interface has already been described withreference to FIG. 33. In various embodiments, the NMR logging module3616 and operator module can communicate via any one of a wired-drillpipe connection, an acoustic telemetry connection, optical communicationand/or electronic communication.

FIG. 37 shows an LWD NMR logging module 3700 for applying multi-segmentsequences to a substance 3702 in accordance with one embodiment of thepresent disclosure. The module 3700 includes a cylindrical magnet 3704that generates a static magnetic field within a zone of sensitivity 3706within the earth formation. The module 3700 also includes a drill collar3708 with an axial slot 3710. A coil 3712 is disposed within the slot3710 and the slot is filled with a ceramic insulator. The slot 3712 issealed using a cover 3714. In some embodiments, the cover 3714 is formedfrom a non-magnetic material and/or non-conductive material. The coil3712 is composed of at least two diametrically opposed conductors. Atone end, the conductors are grounded to the drill collar 3708. At theother end, the conductors are coupled to broadband NMR electronics 3716.The broadband NMR electronics 3716 include a transformer and theconductors are coupled to the transformer via, for example, pressurefeed-throughs. The transformer 3718 maintains a 180 degree phasedifference between the currents in the diametrically oppositeconductors. The coil 3712 applies an oscillating magnetic field to anarea of interest 3720 within the zone of sensitivity 3706. In someembodiments, the oscillating magnetic field is axially symmetric tofacilitate measurements during rotation of the drill string. Inaccordance with exemplary embodiments of the present disclosure, theoscillating field applied to the earth formation includes multi-segmentsequences. In additional or alternative embodiments, the coil 3712 canalso be configured so that the drill collar itself 3708 produces theoscillating magnetic field. Further details of NMR LWD systems aredescribed in U.S. Pat. No. 5,629,623, issued on May 13, 1997.

Various embodiments of the present disclosure are not limited tooilfield borehole applications, such as LWD systems and wirelinesystems. Exemplary embodiments of the present disclosure can also beimplemented in surface environments, such as laboratories. Furthermore,illustrative embodiments are not limited to oil and gas fieldapplications. Various embodiments described herein may also haveapplication in chemical production, food production, material inspectionand infrastructure inspection (e.g., building and bridges). In oneparticular embodiment, cheese can be analyzed using multi-segmentsequences in order to determine an oil-to-water ratio within the cheese.In the specific example of analyzing cheese, a two-dimensionalmeasurement can be made. The efficiency of such a measurement can beincreased using the systems and pulses sequences described above.

Furthermore, the broadband NMR systems and devices described herein,including the transmitter 3214 and the receiver 3206, are not limited toimplementing NMR techniques and sequences. The systems and devicesdescribed herein can also be used to implement other magnetic resonance(MR) techniques and sequences, such as nuclear quadrupole resonance(NQR) techniques and sequences. For example, the receiver 3206 describedherein can be used to process NQR signals that have been obtained from asubstance.

Although several example embodiments have been described in detailabove, those skilled in the art will readily appreciate that manymodifications are possible in the example embodiments without materiallydeparting from the scope of this disclosure. Accordingly, all suchmodifications are intended to be included within the scope of thisdisclosure.

We claim:
 1. A method for applying a nuclear magnetic resonance (NMR)sequence to a substance, the method comprising: applying a staticmagnetic field to the substance; applying an NMR pulse sequence to thesubstance using a non-resonant NMR transmitter circuit, wherein the NMRpulse sequence comprises: a first pulse sequence segment applied at afirst set of frequencies to a first shell; and a second pulse sequencesegment applied at a second set of frequencies to a second shell,wherein the second pulse sequence segment is initiated before the firstshell reaches thermal equilibrium.
 2. The method of claim 1, wherein thefirst shell reaches thermal equilibrium after a time period no greaterthan five times T₁ after the first pulse sequence segment is completed.3. The method according to claim 1, wherein the NMR pulse sequenceincludes: a third pulse sequence segment applied at a third set offrequencies to a third shell, wherein the third pulse sequence segmentis initiated before the second shell reaches thermal equilibrium.
 4. Themethod according to claim 1, wherein a difference between an average ofthe first set of frequencies and an average of the second set offrequencies is greater than 10% of the first set of frequencies.
 5. Themethod according to claim 1, wherein the static magnetic field is aninhomogeneous static magnetic field.
 6. The method according to claim 1,wherein the second pulse sequence segment is at least partiallyinterposed within the first pulse sequence segment.
 7. The methodaccording to claim 1, wherein the first pulse sequence segment generatesa first resonant signal in the first shell and the second pulse sequencesegment generates a second resonant shell in the second shell.
 8. Themethod according to claim 7, further comprising: detecting the firstresonant signal; and detecting the second resonant signal.
 9. The methodaccording to claim 8, further comprising: determining at least one of aT₁ time, a T₂ time, and a diffusion constant for the first shell of thesubstance based upon the first resonant signal; and determining at leastone of a T₁ time, a T₂ time, and a diffusion constant for the secondshell of the substance based upon the second resonant signal.
 10. Themethod according to claim 6, wherein an excitation pulse within thesecond pulse sequence segment is applied with a phase that is differentfrom an excitation pulse within the first pulse sequence.
 11. The methodaccording to claim 1, wherein the NMR pulse sequence includes at leastthree pulse sequence segments that are applied at different frequenciesto three different shells of the substance.
 12. The method according toclaim 11, wherein the at least three pulse sequence segments areinterleaved.
 13. The method according to claim 11, wherein at least twoof the at least three pulse sequence segments are partially interposedwithin the first pulse sequence segment.
 14. The method according toclaim 13, wherein the at least three pulse sequence segments eachinclude an excitation pulse followed by a plurality of refocusing pulsesand the excitation pulses for each of the at least three pulse sequencesare applied with a time interval between each excitation pulse.
 15. Themethod according to claim 14, wherein each excitation pulse appliedsubsequent to the first excitation pulse is applied with a shifted phaseto compensate for the Bloch-Siegert phase shift.
 16. The methodaccording to claim 14, wherein the time interval between each excitationpulse is varied to compensate for the Bloch-Siegert phase shift.
 17. Asystem comprising: a coil for applying a nuclear magnetic resonance(NMR) pulse sequence to a substance; a NMR transmitter comprising anon-resonant NMR transmitter circuit electronically coupled to the coil;a processor; and a memory storing instructions executable by theprocessor to perform processes that include: providing the NMR pulsesequence to the NMR transmitter, wherein the NMR pulse sequencecomprises: a first pulse sequence at a first set of frequencies forapplication to a first shell; and a second pulse sequence at a secondset of frequencies for application to a second shell, wherein the secondpulse sequence segment is configured to be applied before the firstshell reaches thermal equilibrium.
 18. The system of claim 17, whereinthe second pulse sequence is interposed within the first pulse sequence.19. The system of claim 17, further comprising: a NMR receiver that isconfigured to receive resonant signals generated within the substanceand detected at the coil.
 20. The system of claim 19, wherein theresonant signals include: a first resonant signal at a first set offrequencies from the first shell; and a second resonant signal at asecond set of frequencies from the second shell.
 21. The system of claim17, further comprising: a magnet for applying a static magnetic field tothe substance.
 22. The system of claim 17, wherein the system is part ofa borehole tool for investigating earth formations.
 23. The system ofclaim 17, wherein the system is part of a logging-while-drilling toolfor investigating earth formations.
 24. A method for applying a nuclearmagnetic resonance (NMR) sequence to a substance, the method comprising:applying a static magnetic field to the substance; applying an NMR pulsesequence to the substance, wherein the NMR pulse sequence comprises: afirst pulse sequence segment at a first set of frequencies that isapplied to a first shell; and a second pulse sequence segment at asecond set of frequencies that is applied to a second shell, wherein thesecond pulse sequence segment is interposed within the first pulsesequence segment.
 25. A method for applying a nuclear magnetic resonance(NMR) sequence to a substance, the method comprising: applying a staticmagnetic field to the substance; applying an NMR pulse sequence to thesubstance using a non-resonant transmitter circuit, wherein the NMRpulse sequence comprises: a first pulse sequence segment at a first setof frequencies applied to a first set of atomic nuclei; and a secondpulse sequence segment at a second set of frequencies applied to asecond set of atomic nuclei, wherein the first set of atomic nuclei andthe second set of atomic nuclei are different chemical sets of atomicnuclei.
 26. The method according to claim 25, wherein the second pulsesequence segment is initiated before the first set of atomic nucleireach thermal equilibrium.
 27. The method according to claim 25, whereinthe first pulse sequence segment and the second pulse sequence segmentare interposed.
 28. The method according to claim 25, wherein the firstset of atomic nuclei and the second set of atomic nuclei are selectedfrom the group consisting of carbon nuclei, hydrogen nuclei, sodiumnuclei, and fluorine nuclei.
 29. A system comprising: a coil forapplying a nuclear magnetic resonance (NMR) pulse sequence to asubstance; a NMR transmitter comprising a non-resonant NMR transmittercircuit electronically coupled to the coil; a processor; and a memorystoring instructions executable by the processor to perform processesthat include: providing the NMR pulse sequence to the NMR transmitter,wherein the NMR pulse sequence comprises: a first pulse sequence segmentat a first set of frequencies applied to a first set of atomic nuclei;and a second pulse sequence segment at a second set of frequenciesapplied to a second set of atomic nuclei, wherein the first set ofatomic nuclei and the second set of atomic nuclei are different chemicalsets of atomic nuclei.
 30. The system according to claim 29, wherein thesecond pulse sequence segment is initiated before the first set ofatomic nuclei reach thermal equilibrium.
 31. The system according toclaim 29, wherein the first pulse sequence segment and the second pulsesequence segment are interposed.
 32. The system according to claim 29,wherein the first set of atomic nuclei and the second set of atomicnuclei are selected from the group consisting of carbon nuclei, hydrogennuclei, sodium nuclei, and fluorine nuclei.
 33. The system according toclaim 29, wherein the system is part of a borehole tool forinvestigating earth formations.